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Infinite Dimensional Holomorphy
2019We give an introduction to vector-valued holomorphic functions in Banach spaces, defined through Frechet differentiability. Every function defined on a Reinhardt domain of a finite-dimensional Banach space is analytic, i.e. can be represented by a monomial series expansion, where the family of coefficients is given through a Cauchy integral formula ...
Domingo García +2 more
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On some various notions of infinite dimensional holomorphy
Lecture Notes in Mathematics, 1974The aim of the present work is to show that many notions of holomorphic maps in the framework of locally convex spaces (l.c.s.) or bornological vector spaces (b.v.s.) are in fact reducible to only one definition given by J. S. e Silva in [11]. We consider only definitions satisfying the following conditions: 1 ) they generalize the notion of an ...
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Some Aspects of Infinite-Dimensional Holomorphy in Mathematical Physics
North-Holland Mathematical Library, 1986Publisher Summary This chapter discusses some of the aspects of infinite-dimensional holomorphy in mathematical physics. The theory has been very much developed in Banach spaces and also in general locally convex spaces. The chapter illustrates the interconnections between the infinite-dimensional holomorphy theory and applications by recalling two ...
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A glimpse at infinite dimensional holomorphy
Lecture Notes in Mathematics, 1974openaire +3 more sources
Proceedings on Infinite Dimensional Holomorphy
Lecture Notes in Mathematics, 1974openaire +3 more sources
The holomorphic functional calculus and infinite dimensional holomorphy
Lecture Notes in Mathematics, 1974openaire +3 more sources
On a Bornological Structure in Infinite‐Dimensional Holomorphy
Mathematische Nachrichten, 1988AbstractThe bornology (b) of bounded subsets with respect to continuous convergence is used on spaces of holomorphic functions. It is shown that HomcoHb(U) ≅ U for a circled convex open subset U of a complete nuclear space. Exponential laws for spaces of holomorphic functions with bornological structures are proved and the connection with Colombeau's ...
Bjon, S., Lindström, M.
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Appendix I Further Developments in Infinite Dimensional Holomorphy
North-Holland Mathematics Studies, 1981openaire +3 more sources
Characterization of the holomorphy of infinite dimensional domains by Oka's principle
1997openaire +3 more sources
An application of infinite dimensional holomorphy to the geometry of banach spaces
Lecture Notes in Mathematics, 1987openaire +3 more sources