| Title:
|
Holomorphy types and spaces of entire functions of bounded type on Banach spaces (English) |
| Author:
|
Fávaro, Vinícius V. |
| Author:
|
Jatobá, Ariosvaldo M. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
909-927 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper spaces of entire functions of $\Theta $-holomorphy type of bounded type are introduced and results involving these spaces are proved. In particular, we ``construct an algorithm'' to obtain a duality result via the Borel transform and to prove existence and approximation results for convolution equations. The results we prove generalize previous results of this type due to B. Malgrange: Existence et approximation des équations aux dérivées partielles et des équations des convolutions. Annales de l'Institute Fourier (Grenoble) VI, 1955/56, 271--355; C. Gupta: Convolution Operators and Holomorphic Mappings on a Banach Space, Séminaire d'Analyse Moderne, 2, Université de Sherbrooke, Sherbrooke, 1969; M. Matos: Absolutely Summing Mappings, Nuclear Mappings and Convolution Equations, IMECC-UNICAMP, 2007; and X. Mujica: Aplicações $\tau (p;q)$-somantes e $\sigma (p)$-nucleares, Thesis, Universidade Estadual de Campinas, 2006. (English) |
| Keyword:
|
Banach spaces |
| Keyword:
|
holomorphy types |
| Keyword:
|
homogeneous polynomials |
| Keyword:
|
holomorphic functions |
| Keyword:
|
convolution operators |
| Keyword:
|
Borel transform |
| Keyword:
|
approximation and existence theorems |
| MSC:
|
46E50 |
| MSC:
|
46G20 |
| MSC:
|
46G25 |
| MSC:
|
47B38 |
| idZBL:
|
Zbl 1224.46087 |
| idMR:
|
MR2563566 |
| . |
| Date available:
|
2010-07-20T15:48:42Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140525 |
| . |
| Reference:
|
[1] Banach, S.: Théorie des opérations linéaires.Hafner New York (1932). Zbl 0005.20901 |
| Reference:
|
[2] Dineen, S.: Holomorphy types on a Banach space.Stud. Math. 39 (1971), 241-288. Zbl 0235.32013, MR 0304705, 10.4064/sm-39-3-241-288 |
| Reference:
|
[3] Fávaro, V. V.: The Fourier-Borel transform between spaces of entire functions of a given type and order.Port. Math. 65 (2008), 285-309. MR 2428422, 10.4171/PM/1813 |
| Reference:
|
[4] Fávaro, V. V.: Convolution equations on spaces of quasi-nuclear functions of a given type and order.Preprint. |
| Reference:
|
[5] Floret, K.: Natural norms on symmetric tensor products of normed spaces.Note Mat. 17 (1997), 153-188. Zbl 0961.46013, MR 1749787 |
| Reference:
|
[6] Gupta, C.: Convolution Operators and Holomorphic Mappings on a Banach Space. Séminaire d'Analyse Moderne, 2.Université de Sherbrooke Sherbrooke (1969). |
| Reference:
|
[7] Horváth, J.: Topological Vector Spaces and Distribuitions.Addison-Wesley Reading (1966). MR 0205028 |
| Reference:
|
[8] Malgrange, B.: Existence et approximation des équations aux dérivées partielles et des équations des convolutions.Annales de l'Institute Fourier (Grenoble) VI (1955/56), 271-355. MR 0086990 |
| Reference:
|
[9] Martineau, A.: Équations différentielles d'ordre infini.Bull. Soc. Math. Fr. 95 (1967), 109-154 French. Zbl 0167.44202, MR 1507968, 10.24033/bsmf.1650 |
| Reference:
|
[10] Matos, M. C.: On the Fourier-Borel transformation and spaces of entire functions in a normed space.In: Functional Analysis, Holomorphy and Approximation Theory II. North-Holland Math. Studies. G. I. Zapata North-Holland Amsterdam (1984), 139-170. Zbl 0568.46036, MR 0771327, 10.1016/S0304-0208(08)70827-2 |
| Reference:
|
[11] Matos, M. C.: On convolution operators in spaces of entire functions of a given type and order.In: Complex Analysis, Functional Analysis and Approximation Theory J. Mujica North-Holland Math. Studies Vol. 125 North-Holland Amsterdam (1986), 129-171. Zbl 0658.46016, MR 0893415, 10.1016/S0304-0208(08)72168-6 |
| Reference:
|
[12] Matos, M. C.: Absolutely Summing Mappings, Nuclear Mappings and Convolution Equations.IMECC-UNICAMP (2007),\hfil http://www.ime.unicamp.br/rel\_pesq/2007/rp03-07.html. |
| Reference:
|
[13] Mujica, X.: Aplicações $\tau(p;q)$-somantes e $\sigma(p)$-nucleares.Thesis Universidade Estadual de Campinas (2006). |
| Reference:
|
[14] Nachbin, L.: Topology on Spaces of Holomorphic Mappings.Springer New York (1969). Zbl 0172.39902, MR 0254579 |
| Reference:
|
[15] Pietsch, A.: Ideals of multilinear functionals.In: Proc. 2nd Int. Conf. Operator Algebras, Ideals and Their Applications in Theoretical Physics, Leipzin 1983 Teubner Leipzig (1984), 185-199. Zbl 0562.47037, MR 0763541 |
| Reference:
|
[16] Pietsch, A.: Ideals of multilinear functionals.In: Proc. 2nd Int. Conf. Operator Algebras, Ideals and Their Applications in Theoretical Physics, Leipzin 1983 Teubner Leipzig (1984), 185-199. Zbl 0562.47037, MR 0763541 |
| . |
