Holomorphy types and spaces of entire functions of bounded type on Banach spaces

Vinícius V. Fávaro; Ariosvaldo M. Jatobá

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 4, page 909-927
  • ISSN: 0011-4642

Abstract

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In this paper spaces of entire functions of Θ -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 τ ( p ; q ) -somantes e σ ( p ) -nucleares, Thesis, Universidade Estadual de Campinas, 2006.

How to cite

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Fávaro, Vinícius V., and Jatobá, Ariosvaldo M.. "Holomorphy types and spaces of entire functions of bounded type on Banach spaces." Czechoslovak Mathematical Journal 59.4 (2009): 909-927. <http://eudml.org/doc/37966>.

@article{Fávaro2009,
abstract = {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.},
author = {Fávaro, Vinícius V., Jatobá, Ariosvaldo M.},
journal = {Czechoslovak Mathematical Journal},
keywords = {Banach spaces; holomorphy types; homogeneous polynomials; holomorphic functions; convolution operators; Borel transform; approximation and existence theorems; Banach space; holomorphy type; homogeneous polynomial; holomorphic function; convolution operator; Borel transform; approximation theorem; existence theorem},
language = {eng},
number = {4},
pages = {909-927},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Holomorphy types and spaces of entire functions of bounded type on Banach spaces},
url = {http://eudml.org/doc/37966},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Fávaro, Vinícius V.
AU - Jatobá, Ariosvaldo M.
TI - Holomorphy types and spaces of entire functions of bounded type on Banach spaces
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 4
SP - 909
EP - 927
AB - 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.
LA - eng
KW - Banach spaces; holomorphy types; homogeneous polynomials; holomorphic functions; convolution operators; Borel transform; approximation and existence theorems; Banach space; holomorphy type; homogeneous polynomial; holomorphic function; convolution operator; Borel transform; approximation theorem; existence theorem
UR - http://eudml.org/doc/37966
ER -

References

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  9. Martineau, A., 10.24033/bsmf.1650, Bull. Soc. Math. Fr. 95 (1967), 109-154 French. (1967) Zbl0167.44202MR1507968DOI10.24033/bsmf.1650
  10. Matos, M. C., 10.1016/S0304-0208(08)70827-2, In: Functional Analysis, Holomorphy and Approximation Theory II. North-Holland Math. Studies. G. I. Zapata North-Holland Amsterdam (1984), 139-170. (1984) Zbl0568.46036MR0771327DOI10.1016/S0304-0208(08)70827-2
  11. Matos, M. C., 10.1016/S0304-0208(08)72168-6, In: Complex Analysis, Functional Analysis and Approximation Theory J. Mujica North-Holland Math. Studies Vol. 125 North-Holland Amsterdam (1986), 129-171. (1986) Zbl0658.46016MR0893415DOI10.1016/S0304-0208(08)72168-6
  12. Matos, M. C., Absolutely Summing Mappings, Nuclear Mappings and Convolution Equations, IMECC-UNICAMP (2007),http://www.ime.unicamp.br/rel_pesq/2007/rp03-07.html. (2007) 
  13. Mujica, X., Aplicações τ ( p ; q ) -somantes e σ ( p ) -nucleares, Thesis Universidade Estadual de Campinas (2006). (2006) 
  14. Nachbin, L., Topology on Spaces of Holomorphic Mappings, Springer New York (1969). (1969) Zbl0172.39902MR0254579
  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. (1984) Zbl0562.47037MR0763541
  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. (1984) Zbl0562.47037MR0763541

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