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BSc 1985, MSc 1986, PhD 1990 in Mathematics (UCD) |
| Dr. Mellon's research interests are in Complex Analysis, primarily infinite dimensional, studying manifolds with symmetry. These correspond to the Banach spaces whose open unit balls have a transitive group of (biholomorphic) automorphisms, known as the JB*-triples. As such, the area straddles complex analysis, functional analysis and differential geometry. Dr. Mellon has studied these manifolds from several different perspectives: their curvature, the class of holomorphic maps that they admit and differences between the finite and infinite dimensional cases. She has published extensively on JB*-triples. Recent work includes versions of Wolff's classical theorem on these spaces (concerning invariant domains of holomorphic mappings) and work on composition operators. She has several collaborations with C.H. Chu (University College London), S. Dineen and M. Mackey of UCD. Extended Research Visits: (one month or more)
Short Research Visits: (one week or more)
Research Projects Sponsor : Enterprise Ireland Sponsor : Enterprise Ireland Sponsor: Forbairt/The British Council Sponsor : Enterprise Ireland Sponsor: Forbairt/The British Council Sponsor: Enterprise Ireland. Sponsor: Forbairt/The British Council |
| Mellon, P.; (2000) 'An introduction to bounded symmetric domains' In: * (eds). Textos de Matematica. Series B [Texts in Mathematics. Series B]. [Details] |
| Mellon, P.; (1995) 'An introduction to several comple variables' In: * (eds). Textos de Matematica. Serie B [Texts in Mathematics. Series B]. [Details] |
| Mellon, P.; (2004) 'A general Wolff theorem for arbitrary Banach spaces'. Mathematical Proceedings of the Royal Irish Academy, 104A (2):127-142. [Details] |
| Mackey M., Mellon P.; (2000) 'Angular derivatives on bounded symmetric domains'. Israel Journal of Mathematics, 138 :291-315. [Details] |
| Mellon P.; (2000) 'Holomorphic invariance on bounded symmetric domains'. Journal Fur Die Reine Und Angewandte Mathematik, 523 :199-223. [Details] |
| Mackey M., Mellon P.; (1999) 'The quasi-invertible manifold of a ${\rm JB}\sp *$-triple'. Extracta Mathematicae, 14 (1):51-55. [Details] |
| Mellon P.; (1994) 'The polarisation constant for ${\rm JB}\sp *$-triples'. Extracta Mathematicae, 9 (3):160-163. [Details] |
| Mellon P.; (1993) 'Holomorphic curvature of infinite-dimensional symmetric complex Banach manifolds of compact type'. Annales Academiæ Scientiarum Fennicæ Mathematica, 18 (2):299-306. [Details] | |||||||||
| Mackey, M, Mellon, P, ; (2004) 'A Schwarz lemma and composition operators'. Integr Equat Oper Th, 48 (4):511-524. [Details] | |||||||||
| Chu, Cho-Ho; Mellon, Pauline; (1998) 'Jordan structures in Banach spaces and symmetric manifolds'. Expositiones Mathematicae, 16 (2):157-180. [Details] | |||||||||
| Chu, Cho-Ho; Mellon, Pauline; (1997) '${\rm JB}\sp *$-triples have Pe\Iczynski's Property V'. Manuscripta Mathematica, 93 (3):337-347. [Details] | |||||||||
| Chu, Cho-Ho; Mellon, Pauline; (1997) 'The Dunford-Pettis property in $[\rm JB] \sp *$-triples'. Journal of the London Mathematical Society, 55 (3):515-526. [Details] | |||||||||
| Chu, Cho-Ho; Mellon, Pauline; (1997) 'Iteration of compact holomorphic maps on a Hilbert ball'. Proceedings of the American Mathematical Society, 125 (6):1771-1777. [Details] | |||||||||
| Mellon, P.; (1996) 'Symmetric manifolds of compact type associated to the $[zrm JB}\sp *$-triples $C\sb 0(X,Z)$'. Mathematica Scandinavica, 78 (1):19-36. [Details] | |||||||||
| Mellon, P.; (1996) 'Another look at results of Wolff and Julia type for $J\sp*$-algebras'. Journal of Mathematical Analysis and Applications, 198 (2):444-457. [Details] | |||||||||
| Mellon, P.; (1993) 'Dual manifolds fof $[\rm JB}\sp *$-triples of the form $C(X,U)$'. Proceedings of the Royal Irish Academy, 93 (1):27-42. [Details] | |||||||||
| Mackey, M.; Mellon, P.;; (2002) 'On an angular derivative result of Fan'. Proceedings of Royal Irish Academy, 102A (1):115-126. [Details] | |||||||||
| Mackey, M; Mellon, P.; (2001) 'Compact-like manifolds associated to $\rm JB\sp *$-triples'. Manuscripta Mathematica, 106 (2):203-212. [Details] | |||||||||
| Dineen, Sean; Mackey, Micheal; Mellon, Pauline.; (1999) 'The destiny property for $JB\sp *$-triples'. STUDIA MATHEMATICA, 137 (2):143-160. [Details] | |||||||||
| Dineen, Sean; Mellon, Pauline.; (1998) 'Holomorphic functions on symmetric Banach manifolds of compact type are constant'. Mathematische Zeitschrift, 229 (4):753-765. [Details] | |||||||||
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| Year: 1986. Title: NUI Travelling Studentship in Mathematical Science |
| Year: 1996. Title: EPSRC Fellowship (UK) University of London |
| Year: 1996. Title: Research Fellowship, Mathematisches Institut Oberwolfach, Germany |
| Association: Irish, London, European and American Mathematical Societies, Function/Role: Member |
| Association: Irish Mathematical Society, 1994-1997, Function/Role: Secretary |
| Association: Irish Mathematical Society, 1991-1997, Function/Role: Committee Member |
| Mellon P.; (2006) JB*-triples and related topics. [Conference Organising Committee Member], JB*-triples and related topics, UCD , 02-JAN-06 - 02-JAN-06. |
| Mellon P.; (2001) Jordan Structures in Analysis II (Part I was in UK). [Conference Organising Committee Member], Jordan Structures in Analysis II (Part I was in UK), UK , 01-JAN-01 - 01-JAN-01. |
| Mellon P.; (1996) Annual Meeting of Irish Mathematical Society. [Conference Organising Committee Member], Annual Meeting of Irish Mathematical Society, N/A , 01-APR-96 - 01-APR-96. |
| Mellon P.; (1994) Polynomials and Holomorphic Functions on Infinite Dimensional Spaces. [Conference Organising Committee Member], Polynomials and Holomorphic Functions on Infinite Dimensional Spaces, UCD , 04-APR-94 - 04-APR-94. |
| Mellon P.; (1994) Annual Meeting of Irish Mathematical Society. [Conference Organising Committee Member], Annual Meeting of Irish Mathematical Society, N/A , 03-JAN-94 - 03-JAN-94. |
| Employer: UCD: 1986-1987 and 1988-1990 Position: Tutor and Part-time Lecturer |
| Employer: Universität Tübingen: 1987-1988 Position: NUI Travelling Studentship |
| Employer: NUI Maynooth: 1990-1991 Position: Lecturer Temporary |
| Employer: NUI Maynooth: 1991-1992 Position: Lecturer Permanent |
| Employer: UCD: 1992-2002 Position: Lecturer |
| Employer: UCD: 2002-2003 Position: Senior Lecturer |
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| Year 1985 Institution: Qualification: BSc Subject: |
| Year 1990 Institution: Qualification: PhD Subject: |
| Year 1986 Institution: Qualification: MSc Subject: |
Invited Presentations/Lectures/Colloquia:
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| Other Professional Activities: Referee (for, among others, the following international publications): Proceedings of The London Mathematical Society Journal of the London Mathematical Society Quarterly Journal of Mathematics at Oxford Mathematical Reviews Journal of Mathematical Analysis and its Applications Mathematical Proceedings of the Royal Irish Academy Manauscripta Mathematica |
| International Courses Given: (as part of the 1st and 2nd European Course on Complex Analysis and its Applications. These courses were given for Ph.D students of European universities in the Erasmus program.)
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| Various funding awards from, among others: Enterprise Ireland, Forbairt, The Spanish Government, The British Council (International Collaboration Scheme) in the period 1992-2002 Undergraduate scholarships (UCD): Physics, Chemistry 1982; Mathematics, Chemistry 1983; Mathematics 1984; Prize in Mathematics 1985. |
