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Hermann Render

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Biography

Dr. Hermann Render is  Lecturer of Mathematics at UCD since 1.01.2009. He was awarded the degree of Doctor of Science (Habilitation)  in 1994 by the University of Duisburg (Germany). In 1989 he obtained the PhD (Dr. rer. nat)  at the University of Duisburg, and the Diploma in Mathematics in 1986 at the University of Muenster (Germany).

Dr. Render was research fellow in the framework of the Ramon y Cajal Programme  at the University de La Rioja (Spain) from 1.12.2003 to 30.11.2008.

In the period from 1.4.1994 to 30.09.2002 Dr. Render was Assistant Professor (Oberassistent, C1-Position) at the University of Duisburg. From 1.10.2002 to 30.4.2003 Dr. Render  had a position as a C3-Professor (Vertretungsprofessur) at the University of Bonn, Germany.

In 1999/2000 a research fellowship of the Alexander von Humboldt Foundation (Bonn, Germany) was awarded to Dr. Render  in the framework of the Theodor-Lynen Programme. 





 
 

Professional

Honours and Awards

Year: 1999.
Title: Fellowship of the Alexander von Humboldt Foundation (Feodor Lynen)
Year: 1998.
Title: Prize for Excellence Teaching
Year: 1991.
Title: Postdoctoral Fellowship of DFG
Year: 1990.
Title: Ph.D. Extraordinary Prize
Year: 1983.
Title: Member of the ''Studienstiftung des Deutschen Volkes''

Associations

Association: Irish Mathematical Society, Function/Role: Member
Association: American Mathematical Society, Function/Role: Member
     

Conference Contributions

Hermann Render (2011) Multivariate Bernstein operators. [Keynote Address], International Conference on Multivariate Approximation, Hagen, University of Dortmund, Germany , 24-SEP-11 - 27-FEB-11.
Hermann Render (2017) Reflection Principles and Harmonic Extensions. [Invited Oral Presentation], Complex Functions, Operators, Partial Differential Equations and Applications in Mathematical Physics, Mittag-Leffler Institute, Djurshom, Sweden , 11-JUN-17 - 16-JUN-17.
Hermann Render (2015) Fischer Operators and the Khavison-Shapiro Conjecture. [Invited Lecture], Conference Complex Analysis and Dynamical Systems VII, Nahariya, Israel, Nahariya, Israel , 10-MAY-15 - 15-MAY-15.
Hermann Render (2016) The pseudo-positive moment problem and cubatures on the disk. [Invited Lecture], Andrejewski-Tage: Moment Problems in Theoretical Physics, Konstanz, University of Konstanz, Germany , 07-APR-16 - 09-APR-16.
H. Render (2016) Generalized Daubechies wavelets reproducing exponential polynomials. [Oral Presentation], Conference on Harmonic Analysis and Approximation Theory HAAT2016, Barcelona, Centre De Recerca Matematica , 06-JUN-16 - 10-JUN-16.
Hermann Render (2014) Rational Bernstein Operators. [Oral Presentation], V Jaen Conference on Approximation Theory, Ubeda, Spain , 23-JUN-14 - 26-JUN-14.
H. Render (2012) Error Estimates for Polyharmonic Cubutare Formulae. [Invited Lecture], 3rd Dolomites Workshop on Constructive Approximation and Applications, Alba Di Canazei, Italy , 09-SEP-12 - 14-SEP-12.
H. Render (2013) Bernstein-type Operators fixing two polynomials. [Invited Lecture], Constructive Theory of Functions 2013, Sozopol, Bulgaria , 09-JUN-13 - 14-JUN-13.
H. Render (2013) Generalized Daubechies Wavelets and Applications to Image Processing. [Plenary Lecture], HUMBOLDT KOLLEG Digitization of Heritage in Science, Bulgarian Academy of Sciences, Sofia , 01-NOV-13 - 05-NOV-13.
H. Render; (2009) Cauchy and Goursat problems for holomorphic PDE's. [Plenary Lecture], Computational Methods and Function Theory, Ankara, Turkey , 08-JUN-09 - 12-JUN-09.
H. Render; (2008) Invited participation. [Other], Workshop Holomorphic PDE's, small divisors and summability, CIRM, Luminy, Marseille, France , 27-JAN-08 - 02-FEB-08.
H. Render; (2007) Bernstein bases and operators for exponential polynomials. [Invited Lecture], Workshop Approximation and Wavelets, Koenigswinter (bei Bonn), Germany , 01-OCT-07 - 04-OCT-07.
H. Render; (2007) Funciones poliarmonicas y una conjetura de W. Haymany y B. Korenblum. [Invited Lecture], X Encuentros de Analisis Real y Complejo, Palma de Mallorca, Spain , 10-MAY-07 - 13-MAY-07.
H. Render; (2007) Pade approximation for a multivariate Markov transform. [Invited Lecture], Congreso Special Functions, Information Theory and Mathematical Physics, Granada, Spain , 17-SEP-07 - 19-SEP-07.
H. Render; (2006) Real Bargmann spaces, Fischer pairs and Sets of Uniqueness for Polyharmonic Functions. [Invited Lecture], Third International Conference on Complex Analysis and Dynamical Systems, Nahariya, Israel , 02-JAN-06 - 06-JAN-06.
H. Render; (2006) Constructive Methods in Geometric Modeling. [Invited Lecture], Advanced Nato Research Workshop: Scientific Support for the Decison Making in the Security Sector, Velingrad, Bulgaria , 21-OCT-06 - 25-OCT-06.
H. Render; (2006) Entire solutions for the Dirichlet problem and a characterization of ellipsoids. [Poster Presentation], Recent Advances in Nonlinear Partial Differential Equations and Applications,Conference in honor of P. Lax and L. Nirenberg, Toledo, Spain , 07-JUN-06 - 10-JUN-06.
H. Render; (2005) Extended cubature formulae of Gauss-Jacobi type for a certain class of measures. [Invited Lecture], 6th International Conference on Multivariate Approximation, Haus Bommerholz, Dortmund, Germany , 25-SEP-05 - 01-OCT-05.
H. Render; (2005) Optimization of homogeneous polynomials on the simplex and the sphere. [Invited Lecture], 10th Workshop on Well-posedness of Optimzation Problems and Related Topics, Borovets, Bulgaria , 05-SEP-05 - 09-SEP-05.
H. Render; (2004) Polysplines -- A PDE-approach to Multivariate Spline Analysis. [Invited Lecture],  Second International Conference on Computational Harmonic Analysis, Vanderbilt University, Tennessee, USA , 24-MAY-04 - 30-MAY-04.
H. Render; (2004) PDE-methods in Multivariate Spline Analysis. [Invited Lecture],  Generalized Functions 2004, Topics in PDE, Harmonic Analysis and Mathematical Physics, Novi Sad, Serbia , 22-SEP-04 - 28-SEP-04.
H. Render; (2003) Polysplines auf Streifengebieten. [Invited Lecture], 13. Rhein-Ruhr-Workshop ueber Angewandte Analysis, Approximationstheorie, CAGD und Numerische Mathematik, Burg Gemen, Germany , 14-FEB-03 - 15-FEB-03.
H. Render; (2003) Interpolation with polyharmonic cardinal splines. [Invited Lecture], International Congress MASSEE 2003, Borovets, Bulgaria , 15-SEP-03 - 21-SEP-03.
H. Render; (2002) Polysplines -- A new method in CAGD. [Invited Lecture], Fifth International Conference on Curves and Surfaces, Saint-Malo, France , 27-JUN-02 - 03-JUL-02.
H. Render; (2001) Multiresolutional Analysis via cardinal Polysplines. [Invited Lecture], International Conference of Complex Analysis and Dynamical Systems, ORT Braude College, Karmiel, Israel , 19-JUN-01 - 22-JUN-01.
H. Render; (2001) Rotation invariant Multiresolutional Analysis and cardinal Polysplines. [Invited Lecture], International Conference of Computational Harmonic Analysis, Hongkong , 04-JUN-01 - 08-JUN-01.
 

Employment

Employer: Universidad de La Rioja (Spain)
Position: Investigador de Ramon y Cajal
Employer: University of Duisburg (Germany)
Position: Assistant Professor (C2 Position)
Employer: University of Bonn (Germany)
Position: Assistant Professor
Employer: Bulgarian Academy of Sciences (Bulgaria)
Position: Visiting Professor
Employer: University of Duisburg (Germany)
Position: Research Assistant (C1-position)

Education

Year 1989 Institution: University of Duisburg (Germany)
Qualification: Dr rer nat Subject: Mathematics
Year 1994 Institution: Gerhard Mercator University of Duisburg, Germany
Qualification: HABILITATION Subject:
Year 1986 Institution: University of Muenster (Germany)
Qualification: Diplom Subject: Mathematics
Year 1989 Institution: Gerhard Mercator University of Duisburg, Germany
Qualification: PhD Subject:
Year 1986 Institution: University of Munster (WWilhe), Germany
Qualification: Dip Mathematiker Subject:

Languages

Spanish:
Bulgarian:
English:
German:
       

Publications

     

Peer Reviewed Journals

Gardiner, S.J., Render, H. (2018) 'Extension results for harmonic functions which vanish on cylindrical surfaces'. Analysis and Mathematical Physics, . [DOI] [Details]
Gardiner, S.J., Render H. (2019) 'Harmonic functions which vanish on coaxial cylinders'. Journal d'Analyse Mathematique, . [Details]
O. Kounchev, H. Render (2017) 'A symmetry property for polyharmonic functions vanishing on equidistant hyperplanes'. Mathematische Nachrichten, 290 :1087-1096. [DOI] [Details]
H. Render (2016) 'A Characterization of the Khavinson-Shapiro Conjecture Via Fischer Operators'. Potential Analysis, . [DOI] [Details]
D. Khavinson, E. Lundberg, H. Render (2016) 'Dirichlet's Problem with Entire Data Posed on an Ellipsoidal Cylinder'. Potential Analysis, . [DOI] [Details]
D. Khavinson, E. Lundberg, H. Render (2017) 'The Dirichlet problem for the slab with entire data and a difference equation for harmonic functions'. Canadian Mathematics Bulletin, 60 :146-153. [DOI] [Details]
S.J. Gardiner, H. Render (2016) 'A reflection result for harmonic functions which vanish on a cylindrical surface'. J. Math. Analysis Appl, 443 :81-91. [DOI] [Details]
S. Gardiner, H. Render (2015) 'Harmonic functions which vanish on a cylindrical surface'. J. Math. Analysis Appl, . [DOI] [Details]
N. Dyn, O. Kounchev, D. Levin, H. Render (2014) 'Regularity of generalized Daubechies wavelets reproducing exponential polynomials with real-valued parameters'. Applied and Computational Harmonic Analysis, 37 (288-306). [DOI] Link to full text [Details]
H. Render (2014) 'Convergence of rational Bernstein operators'. Applied Mathematics and Computation, 232 :1076-1089. [DOI] Link to full text [Details]
O. Kounchev, Hermann Render (2013) 'Polyharmonic functions of infinite order on annular regions'. Tohoku Math, 65 :199-299. [DOI] Link to full text [Details]
Hermann Render (2013) 'Harmonic Divisors and rationality of zeros of Jacobi polynomials'. Ramanujan Journal, 31 :257-270. [DOI] Link to full text [Details]
O. Kounchev, H. Render (2012) 'Polyharmonic Hardy spaces on the complexified annulus and error estimates of cubature formulas'. Results Mathematics, 62 :377-403. [DOI] Link to full text [Details]
Ghergu, M. and Render, H.; (2012) 'Positivity property for the clamped plate problem on the ellipse and strip'. Mathematische Nachrichten, 185 :1052-1062. Available Online [DOI] [Details]
E. Lundberg, H. Render ; (2011) 'The Khavinson-Shapiro Conjecture and Polynomial Decompositions'. J. Math. Analysis Appl, 376 :506-513. [DOI] Link to full text [Details]
O. Kounchev, H. Render; (2010) 'The moment problem for pseudo-positive definite functionals'. Arkiv for Matematik, 48 :97-120. [DOI] [Details]
Aldaz, JM,Render, H; (2010) 'Optimality of generalized Bernstein operators'. Journal of Approximation Theory, 162 :1407-1416. [DOI] [Details]
Render, H; (2010) 'Cauchy, Goursat and Dirichlet problems for holomorphic partial differential equations'. Computational Methods and Function Theory, 10 :519-554. [DOI] Link to full text [Details]
J.M. Aldaz, O. Kounchev, H. Render; (2010) 'Bernstein operators for Extended Chebyshev systems'. Applied Mathematics and Computation, 162 :790-800. [DOI] [Details]
J.M. Aldaz, O. Kounchev, H. Render; (2009) 'Bernstein operators for exponential polynomials'. Constructive Approximation, 29 :345-367. [DOI] Link to full text [Details]
J. M. Aldaz, O. Kounchev, H. Render; (2009) 'Shape preserving properties of generalized Bernstein operators on extended Chebyshev spaces'. Numer. Math, 114 :1-25. [DOI] Link to full text [Details]
O. Kounchev, H. Render; (2009) 'On the Bernstein operator of S. Morigi and M. Neamtu'. Results in Mathematics, 53 :311-322. [DOI] Link to full text [Details]
P. Ebenfelt, H. Render ; (2008) 'The Goursat Problem for a Generalized Helmholtz Operator in the plane'. Journal d'Analyse Mathematique, 105 :149-168. [DOI] Link to full text [Details]
P. Ebenfelt, H. Render ; (2008) 'On the mixed Cauchy problem with data on singular conics'. Journal of the London Mathematical Society, 78 :248-266. [DOI] Link to full text [Details]
H. Render; (2008) 'Reproducing kernels for polyharmonic polynomials'. Archiv der Mathematik, 91 :136-144. [DOI] Link to full text [Details]
H. Render; (2008) 'Real Bargmann spaces, Fischer decompositions and Sets of uniqueness for polyharmonic functions'. Duke Math. J, 142 :313-351. [DOI] Link to full text [Details]
O. Kounchev, H. Render; (2008) 'Pade approximation for a multivariate Markov transform'. Journal of Computational and Applied Mathematics, 219 :416-430. [DOI] Link to full text [Details]
A. Bejancu, O. Kounchev, H. Render ; (2007) 'Cardinal interpolation with periodic  polysplines on strips'. Calcolo, 44 :203-218. [DOI] [Details]
O. Kounchev, H. Render; (2007) 'Convergence of polyharmonic splines on semi-regular grids Z x aZ^n  for a to 0'. Numerical Algorithms, 44 :255-272. [DOI] Link to full text [Details]
O. Kounchev, H. Render; (2007) 'Polyharmonicity  and algebraic support of measures'. Hiroshima Math. J, 37 :25-44. Link to full text [Details]
J. M. Aldaz, O. Kounchev, H. Render ; (2007) 'On real-analytic recurrence relations for cardinal exponential B-splines'. Journal of Approximation Theory, 145 :253-265. [DOI] Link to full text [Details]
O. Kounchev, H. Render; (2005) 'Polyharmonic splines on grids Z x aZ ^n and their limits'. Mathematics of Computation, 74 :1831-1841. [DOI] [Details]
O. Kounchev, H. Render; (2005) 'Cardinal Interpolation with polysplines on annuli'. Journal of Approximation Theory, 137 :89-107. [DOI] [Details]
O. Kounchev, H. Render; (2004) 'The approximation order of polysplines'. Proceedings of the American Mathematical Society, 132 :455-461. [DOI] Link to full text [Details]
H. Render, A. Todd; (2004) 'Continuous function spaces, (db)-spaces and strongly Hewitt spaces'. Topology and its Applications, 141 :171-186. [DOI] [Details]
H. Render, L. Rogge; (2004) 'Pointwise measurable functions'. Mathematica Scandinavica, 95 :305-319. [DOI] [Details]
H. Render; (2001) 'Sigma-homomorphisms from the Borel sigma-algebra into the Loeb sigma-algebra'. Annals of Pure and Applied Logic, 111 :15-21. [DOI] [Details]
A. Sauer, H. Render ; (2000) 'Multipliers on vector spaces of holomorphic functions'. Nagoya Math. J, 159 :167-178. [Details]
R. Brueck, H. Render; (2000) 'Invertibility of holomorphic functions with respect to the Hadamard product'. Complex Variables, 42 :207-223. [Details]
J.M. Aldaz, H. Render; (2000) 'Borel measure extensions of measures defined on sub-sigma algebras'. Advances in Mathematics, 150 :233-263. [DOI] [Details]
A. Sauer, H. Render; (1999) 'Maximal domains of summability'. Analysis, 19 :207-216. [DOI] [Details]
H. Render; (1999) 'The maximal ideal space of  H^oo (D ) with respect to the Hadamard product'. Proceedings of the American Mathematical Society, 127 :1409-1411. [DOI] [Details]
S. Huang, H. Render, M. Wolff; (1999) 'On the convergence of  sequences of  operators and the convergence of the sequence of their spectra'. Mathematica Scandinavica, 85 :71-78. [DOI] [Details]
H. Render; (1999) 'The property (db) on continuous function spaces'. Topology and its Applications, 92 :101-106. [DOI] [Details]
H. Render; (1998) 'Generalized uniform spaces and applications to function spaces'. Studia Scient. Math. Hungarica, 34 :429-443. [Details]
H. Render; (1997) 'Topological algebras with an orthogonal total sequence'. Colloquium Mathematicum, 72 :215-221. [DOI] [Details]
H. Render; (1997) 'Hadamard's multiplication theorem -- Recent developments'. Colloquium Mathematicum, 74 :79-92. [DOI] [Details]
A. Sauer, H. Render ; (1996) 'Invariance properties of homomorphisms on algebras  of holomorphic functions with the  Hadamard product'. Studia Mathematica, 121 :53-65. [DOI] [Details]
A. Sauer, H. Render; (1996) 'Algebras of holomorphic functions with the Hadamard product'. Studia Mathematica, 118 :77-100. [DOI] [Details]
H. Stroetmann, H. Render; (1996) 'Liapunov`s convexity theorem for topological  measures'. Archiv der Mathematik, 67 :331-336. [DOI] [Details]
H. Render; (1996) 'Hausdorff completions of quasi-uniform spaces'. Czechoslovak Mathematical Journal, 46 :309-316. [Details]
H. Render; (1996) 'A nonstandard approach to realcompactness with applications to the equation v( X x Y ) = v(X) x v(Y)'. Topology and its Applications, 68 :205-239. [DOI] [Details]
H. Render; (1995) 'Countably determined sets and a conjecture of C.W. Henson'. Mathematische Annalen, 303 :307-324. [DOI] [Details]
H. Render; (1995) 'Spaces with a Borel-complete Stone-Cech compactification'. Czechoslovak Mathematical Journal, 45 :325-326. [Details]
H. Render; (1995) 'Covering functions and  the inverse standard part map'. Mathematica Japonica, 42 :301-318. [Details]
H. Render; (1995) 'Nonstandard methods of completing quasi-uniform spaces'. Topology and its Applications, 62 :101-125. [DOI] [Details]
H. Render; (1993) 'Nonstandard topology on function spaces with applications to hyperspaces '. Transactions of the American Mathematical Society, 336 :101-119. [DOI] [Details]
H. Render; (1993) 'Pushing down Loeb measures'. Mathematica Scandinavica, 72 :61-84. [DOI] [Details]
H. Render; (1993) 'On the product of  k- and l-spaces'. Studia Scient. Math. Hungarica, 28 :453-455. [Details]
H. Render; (1992) 'Lattice structures of ordered Banach algebras'. Illinois Journal of Mathematics, 36 :238-250. [Details]
H. Render; (1991) 'Local compactness of function spaces'. Archiv der Mathematik, 56 :286-287. [DOI] [Details]
H. Render; (1991) 'A topological approach to multi-valued Ascoli Theory'. Rendiconti Del Circolo Matematico Di Palermo, Series Ii, 40 :357-370. [DOI] [Details]
H. Render; (1990) 'Extreme positive operators on involution algebras '. Colloquium Mathematicum, 58 :81-96. [DOI] [Details]
H. Render; (1989) 'A characterization of  C*-algebras via positive operators'. Archiv der Mathematik, 52 :379-383. [DOI] [Details]
H. Render; (1989) 'An order theoretic approach to involutive algebras'. Studia Mathematica, 92 :177-186. [DOI] [Details]
H. Render; (1989) 'The radical of a Banach algebra with a closed cone'. Rendiconti del Circolo Matematico di Palermo, 38 :152-154. [DOI] [Details]
 

Conference Publications

O. Kounchev, H. Render (2013) Error Estimates For Polyharmonic Cubature Formulas 3rd Dolomites Workshop on Constructive Approximation and Applications (DWCAA 12) Dolomites Research Notes on Approximation, Volume 6, , pp.62-73 [Details]
O. Kounchev, H. Render (2012) Polyharmonic Hardy spaces on the Klein-Dirac quadric with application to polyharmonic interpolation and cubature formulas International Conference on Partial Differential Equations and Applications , pp.147-176 [Details]
O. Kounchev, H. Render (2008) Holomorphic continuation via Laplace-Fourier series International Conference on Complex Analysis and Dynamical Systems III, Nahariya, Isarel, 2--6.1.2006 [Details]
O. Kounchev, H. Render; (2007) New methods in Geometric Modelling and Controlling Exponential Processes Nato Advanced Research Workshop: Scientific Support for the Decision Making in the Security Sector, Velingrad, Bulgaria , 21-OCT-06 - 25-OCT-06 , pp.144-179 [Details]
K. Alexiev, O.Kounchev, H. Render; (2004) Stable recurrence relations for a class of L-splines and for polysplines Geometric Modeling and Computing: Seattle 2003 Mod. Methods Math., Nashboro Press, Brentwood, TN, , pp.1-12 [Details]
A. Bejancu, O. Kounchev, H. Render; (2003) Cardinal Interpolation with biharmonic polysplines on strips Curve and surface fitting (Saint-Malo, 2002) Mod. Methods Math., Nashboro Press, Brentwood, TN, , pp.41-58 [Details]
O. Kounchev, H. Render; (2002) Wavelet Analysis of cardinal L-splines and Construction of multivariate Prewavelets Approximation theory, X (St. Louis, MO, 2001)  Innov. Appl. Math., Vanderbilt Univ. Press, Nashville, TN, , pp.333-353 [Details]
O. Kounchev, H. Render; (2001) Symmetry properties for cardinal L-splines with applications to polysplines Trends in approximation theory (Nashville, TN, 2000) Innov. Appl. Math., Vanderbilt Univ. Press, Nashville, TN, , pp.191-202 [Details]
S. Ng, H. Render; (2001) The Puritz order and its relationship to the Rudin-Keisler order Reuniting the antipodes---constructive and nonstandard views of the continuum (Venice, 1999) Synthese Lib., 306, Kluwer Acad. Publ., Dordrecht, , pp.157-166 [Details]
H. Render (1996) Homomorphisms on Hadamard Algebras 3rd International Conference on Functional Analysis and Applications, Acquafredda di Maratrea, Italy, 23--28.9.1996 Suppl. Rend. Circ. Mat. Palermo, Serie II, Suppl. 40, , pp.153-158 [Details]
H. Render; (1994) Nonstandard polynomials in several variables . In: S. Albeverio, W.A.J. Luxemburg, M. Wolff eds. International Conference on Applications of Nonstandard Analysis  to Analysis, Functional Analysis and Probability Theory,   Blaubeuren, 19.7.--25.7.1992 Advances in Analysis, Probability and Mathematical Physics - Contributions of Nonstandard Analysis, [Details]
                                                                                                                                       

Research

Research Interests

My research area refers to several different subjects in Pure and Applied Mathematics. Generally speaking, I am interested in applications of mathematics which are based on  methods developed in the theory of Partial Differential Equations (PDE). My interests focus on:

 

  1. Harmonic and polyharmonic functions
  2. Potential theory
  3. Singularities of analytical solutions of PDE¿s
  4. Multivariate Spline Theory
  5. Wavelet Analysis and Sampling Theory
  6. Quadratures, cubatures and moment problems
  7. Geometric Modeling

 

The Theory of PDE's is a vast area which has undergone several changes in the last decades. My interests ly in analytical aspects in this theory, in particular a better understanding of the analytical behaviour of solutions for analytical data functions. In this connection I solved positively in 2008 the Khavinson-Shapiro conjecture for a large class of domains saying that ellipsoids are the the only bounded domains in Euclidean space in this class allowing entire solutions for the Dirichlet problem for entire data functions. This result  was published in 2008 in a top mathematical journal (Duke Math. Journal, rank 10 of 280). A cooperation with Prof. P. Ebenfelt (University of California San Diego) has lead to two more important papers on a related subject.

Quadrature and cubature formula are simple rules for approximating integrals, a basic and important theme in numerical analysis. In cooperation with Prof. Kounchev (Bulgarian Academy of Sciences) we developed a new method based on Fourier-Laplace

Expansion and univariate quadrature formula for Chebyshev systems.

A new direction of research are so-called polyharmonic (multivariate) subdivision schemes which are based on nonstationary subdivision schemes for exponential polynomials. In cooperation with two leading experts, Prof. Nira Dyn and Prof. David Levin (Tel Aviv University) and Prof. Kounchev (Bulgarian Academy of Sciences) we have completed two papers on this subject (supported by the Seed Funding Scheme).  

Research Projects

Sponsor : Science Foundation Ireland (SFI)
Title : International Conference on Complex Analysis, Potential Theory and Applications
Start Date / End Date : 16-FEB-18 / 15-JUN-18
Sponsor : University College Dublin (UCD)
Title : OBRSS Research Support Scheme
Start Date / End Date : 01-NOV-16 / 31-OCT-19
Sponsor : University College Dublin (UCD)
Title : Generalized Daubechies Wavelets
Start Date / End Date : 01-APR-16 / 30-SEP-17
Sponsor : University College Dublin (UCD)
Title : PDE-Methods in Geometric Modeling
Start Date / End Date : 17-MAY-10 / 16-NOV-11

Recent Postgraduates

 

Teaching

Teaching Philosophy

Modules Coordinated

201700   MST10040     Mathematical Studies: Combi & Number Theory
201700   MATH10320     Mathematics: Mathematical Analysis
201700   MATH10230     Mathematics: Mathematics for Agriculture I
       

Collaborators

Internal Collaborators

 
  •     Dr M. Ghergu (UCD)
  •     Prof. S.J.  Gardiner (UCD) 

External Collaborators

  • Prof. O. Kounchev (Bulgarian Academy of Sciences, Bulgaria)
  • Prof. P. Ebenfelt (University California of San Diego, USA)
  • Prof. J. M. Aldaz (Universidad Autonoma, Madrid)
  • Prof. A. Sauer (Fachhochschule Dortmund, Germany)
  • Prof. E. Lundberg (Florida Atlantic University, USA)
  • Prof. N. Dyn (University of Tel Aviv, Israel)
  • Prof. D. Levin (University of Tel Aviv, Israel)
  • Prof. D. Khavinson (University of South Florida, USA)