no. 1-3
Entire functions on locally convex spaces and convolution operators
Compositio Mathematica, Tome 44 (1981) no. 1-3, pp. 145-181 
@article{CM_1981__44_1-3_145_0,
     author = {Matos, Mario C. and Nachbin, Leopoldo},
     title = {Entire functions on locally convex spaces and convolution operators},
     journal = {Compositio Mathematica},
     pages = {145--181},
     year = {1981},
     publisher = {Sijthoff et Noordhoff International Publishers},
     volume = {44},
     number = {1-3},
     mrnumber = {662461},
     zbl = {0485.46022},
     language = {en},
     url = {https://www.numdam.org/item/CM_1981__44_1-3_145_0/}
}
TY  - JOUR
AU  - Matos, Mario C.
AU  - Nachbin, Leopoldo
TI  - Entire functions on locally convex spaces and convolution operators
JO  - Compositio Mathematica
PY  - 1981
SP  - 145
EP  - 181
VL  - 44
IS  - 1-3
PB  - Sijthoff et Noordhoff International Publishers
UR  - https://www.numdam.org/item/CM_1981__44_1-3_145_0/
LA  - en
ID  - CM_1981__44_1-3_145_0
ER  - 
%0 Journal Article
%A Matos, Mario C.
%A Nachbin, Leopoldo
%T Entire functions on locally convex spaces and convolution operators
%J Compositio Mathematica
%D 1981
%P 145-181
%V 44
%N 1-3
%I Sijthoff et Noordhoff International Publishers
%U https://www.numdam.org/item/CM_1981__44_1-3_145_0/
%G en
%F CM_1981__44_1-3_145_0
Matos, Mario C.; Nachbin, Leopoldo. Entire functions on locally convex spaces and convolution operators. Compositio Mathematica, Tome 44 (1981) no. 1-3, pp. 145-181. https://www.numdam.org/item/CM_1981__44_1-3_145_0/

[1] R. Aron: Holomorphy types for open subsets of a Banach space. Studia Math. 45 (1973) 273-289. | Zbl | MR

[2] R. Aron: Tensor products of holomorphic functions, Nederl. Akad. Wetensch. Indag. Math. 35 (76) (1973), Fasc. 3, 192-202. | Zbl | MR

[3] T. Abuabara: A version of the Paley-Wiener-Schwartz theorem in infinite dimensions. Advances in Holomorphy. (J.A. Barroso, editor), North-Holland Publishing Co., (1979) 1-29. | Zbl | MR

[4] V. Bargmann: On a Hilbert space of analytic functions and an associated integral transform, II. A family of related function spaces. Application to distribution theory. Comm. Pure Appl. Math., 20 (1967) 1-101. | Zbl | MR

[5] F.A. Berezin: The Method of second quantization, Nauka, Moscow, (1965). English transl., Pure and Appl. Physics, Vol. 24, Academic Press, New York, (1966). | Zbl | MR

[6] P. Berner: Convolution operators and surjective limits. Advances in Holomorphy (Editor J.A. Barroso) North-Holland Publishing Co. (1979), 93-102. | Zbl | MR

[7] M. Bianchini: Tipos de Silva-holomorfia, Transformadas de Borel e Operadores Diferenciais Parciais-Tese-Universidade Estadual de Campinas, (1978), Brasil.

[8] Ph J. Boland: Espaces pondérés de fonctions entières et de fonctions entières nucléaires sur un espace de Banach, C. R. Acad. Sci. Paris, Sér. A-B, 275 (1972) A-587-A-590. | Zbl | MR

[9] Ph. J. Boland: Some spaces of entire and nuclearly entire functions on a Banach space, Part I-J. Reine Angew. Math. 270 (1974), 38-60.Part II- J. Reine Angew. Math. 271 (1974), 8-27. | Zbl

[10] Ph. J. Boland: Malgrange theorem for entire functions on nuclear spaces: Proc. on Infinite-Dimensional Holomorphy (Editors: T.L. Hayden & T.J. Suffridge), Lecture Notes in Math. Vol. 364, Springer-Verlag, (1974), 135-144. | Zbl | MR

[11] Ph. J. Boland: Holomorphic functions on DFN-spaces. Sém. Pierre Lelong 1973/74. Lecture Notes in Math., Vol. 474, Springer-Verlag (1975) 109-113. | Zbl | MR

[12] Ph. J. Boland: Holomorphic functions on nuclear spaces. Publicaciones del Departamento de Analisis Matematico. Universidad de Santiago de Compostela, Serie B, No. 16, (1976), Spain. | MR

[13] Ph. J. Boland: Some Spaces of Nuclearly Holomorphic Functions of Bounded Type, Atas 3a Quinzena de Análise Funcional e Equações Diferenciais Parciais, Vol. 2, (1971) 175-189. Sociedade Brasileira de Matemática, Brasil.

[14] Ph. J. Boland and S. Dineen: Convolution Operators on G-holomorphic functions in infinite dimensions. Trans. Amer. Math. Soc. 190 (1974), 313-323. | Zbl | MR

[15] J.F. Colombeau: Holomorphy in locally convex spaces and operators on the Fock spaces. To appear in Seminaire Lelong 1977/78 and 78/79. | Zbl | MR

[16] J.F. Colombeau: Differentiable mappings on real nuclear Silva spaces and applications. To appear in Revue Roumaine de Math. Pures et Appliquées. | Zbl | MR

[17] J.F. Colombeau: A result of existence of holomorphic maps which admit a given asymptotic expansion. Advances in Holomorphy (Editor: J.A. Barroso), North-Holland Publishing Company (1979), 221-232. | Zbl | MR

[18] J.F. Colombeau and B. Perrot: Convolution equations in spaces of infinite dimensional entire functions of exponential and related types. To appear in the Trans. Amer. Math. Soc. | Zbl | MR

[19] J.F. Colombeau and B. Perrot: Théorèmes de noyaux analytiques en dimension infinie. C. R. Acad. Sci. Paris, t. 284 (1977), Série A, 759-762. | Zbl | MR

[20] J.F. Colombeau and B. Perrot: Transformation de Fourier Borel et noyaux en dimension infinie. C.R. Acad. Sci. Paris, t. 284 (1977), Série A, 963-966. | Zbl | MR

[21] J.F. Colombeau and B. Perrot: Infinite dimensional holomorphic "normal forms" of operators on the Fock spaces of Boson fields and an extension of the concept of Wick product. Advances in Holomorphy. (Editor: J.A. Barroso) North-Holland Publis. Co. (1979), 249-274. | Zbl | MR

[22] J.F. Colombeau and B. Perrot: Transformation de Fourier-Borel et réflexivité dans les espaces d'applications Silva-analytiques à valeurs vectorielles; applications. C. R. Acad. Sci. Paris, t. 285 (1977), Série, A, 19-21. | Zbl | MR

[23] J.F. Colombeau and B. Perrot: The Fourier-Borel transform in infinitely many dimensions and applications. To appear. | Zbl | MR

[24] J.F. Colombeau: Infinite dimensional C∞ mappings with a given sequence of derivatives at a given point. To appear in Journal of Math. Anal. and Appl. | Zbl

[25] J.F. Colombeau, T.A.W. Dwyeriii and B. Perrot: On the solvability of differential equations of infinite order in non-metrizable spaces. To appear.

[26] J.F. Colombeau and M.C. Matos: Convolution equations in spaces of infinite dimensional entire functions. To appear. | Zbl | MR

[27] J.F. Colombeau and M.C. Matos: On some spaces of entire functions defined on infinite dimensional spaces. To appear. | Zbl | MR

[28] J.F. Colombeau and B. Perrot: Reflexivity and kernels in infinite dimensional holomorphic. To appear in Portugaliae Mathematica. | Zbl | MR

[29] J.F. Colombeau and B. Perrot: The ∂ equation in DFN spaces. Journal of Mathematical Analysis and Applications. To appear.

[30] J.F. Colombeau and J. Mujica: Existence of holomorphic mappings with prescribed asymptotic expansions at a given set of points in infinite dimensions. To appear in Journal of Nonlinear Analysis Theory, Methods and Applications. | Zbl | MR

[31] S. Dineen: Holomorphic functions on a Banach space. Bull. Amer. Math. Soc. 76 (1970), 883-886. | Zbl | MR

[32] S. Dineen: Holomorphic types on a Banach space. Studia Math. 39 (1971), 241-288. | Zbl | MR

[33] T.A.W. Dwyer Iii.: Vector-valued convolution equations for the nuclear holomorphy type. Proc. Royal Irish Academy, Vol 76, sect A, (1976), 101-110. | Zbl | MR

[34] T.A.W. Dwyer Iii.: Convolution equations for vector-valued entire functions of nuclear bounded type. Trans Amer. Math. Soc. 217 (1976), 105-119. | Zbl | MR

[35] T.A.W. Dwyer Iii.: Differential operators of infinite order in locally convex spaces. I. Rendiconti di Matematica (1), Vol. 10, Serie VI (1977), 149-179.II Rendiconti di Matimatica (2-3), Vol. 10. Serie VI (1977), 273-293. | Zbl | MR

[36] T.A.W. Dwyer Iii.: Holomorphic Fock representation and partial differential equations on countably Hilbert spaces. Bull. Amer. Math. Soc., 79, No. 5 (1975), 1045-1050. | Zbl | MR

[37] T.A.W. Dwyer Iii.: Partial differential equations in Fischer-Fock spaces for the Hilbert-Schmidt holomorphy type. Bull. Amer. Math. Soc. 77 (1971), 725-730. | Zbl | MR

[38] T.A.W. Dwyer Iii.: Holomorphic representation of tempered distributions and weighted Fock spaces. Analyse Fonctionnelle et Applications (Éditeur: L. Nachbin), Actualités Scient. Indust. 1367, Hermann (1975), 95-118. | Zbl | MR

[39] T.A.W. Dwyer Iii.: Partial differential equations in holomorphic Fock spaces. Functional Analyses and Applications (Editor: L. Nachbin). Lecture Notes in Math. Springer-Verlag, 384 (1974), 252-259. | Zbl | MR

[40] T.A.W. Dwyer Iii.: Dualité des espaces de fonctions entières en dimension infinie. C. R. Acad. Sci. Paris, Ser. A, 280 (1975), 1439-1442. | Zbl | MR

[41] T.A.W. Dwyer Iii.: Equations différentielles d'ordre infini dans des espaces localement convexes. C. R. Acad. Sci. Paris, 281 (1975), Ser. A, 163-166. | Zbl

[42] T.A.W. Dwyer Iii.: Dualité des espaces de fonctions entières en dimension infinie. Ann. Inst. Fourier(Grenoble) 2 (No. 4) (1976), 151-195. | Zbl | MR | Numdam

[43] T.A.W. Dwyer Iii.: Infinite Dimensional Analytic Systems. Proceedings of the 1977, IEEE Conference on Decision and Control (1977), 285-290. | MR

[44] T.A.W. Dwyer Iii.: Differential equations of infinite order in vector-valued holomorphic Fock spaces. Infinite Dimensional Holomorphy and Applications (Editor: M.C. Matos), North-Holland Publishing Co., Amsterdam (1977), 167-200. | Zbl | MR

[45] T.A.W. Dwyer Iii.: Fourier-Borel duality and bilinear realizations of control systems. Proceedings of the 1976. Ames (NASA). Conference on Geometric Methods in Control. Math. Sci. Press, 53 Jordan Rd., Brookline, Ma. (1977), 405-438. | Zbl | MR

[46] T.A.W. Dwyer Iii.: Analytic Evolution Equations in Banach spaces. Proceedings of the 1977, Dublin Conference on Vector Space Measures and Applications, Part II, (Editores: R.M. Aron & S. Dineen). Lecture Notes in Math. 645, Springer-Verlag (1978). | Zbl | MR

[47] C.P. Gupta: On Malgrange theorem for nuclearly entire functions on a Banach space. Proc. Acad. Sci. Amsterdam A-73, Indag. Math. (1970), 356-358. | Zbl | MR

[48] C.P. Gupta: Convolution operators and holomorphic mappings on a Banach space. Séminare d'Analyse Moderne, No. 2, Université de Sherbrooke, Sherbrooke (1969). | Zbl

[49] C.P. Gupta: Malgrange theorem for nuclearly entire functions of bounded type on a Banach space. Notas de Matemática, Vol. 37 (1968), Instituto de Mathemática Pura e Aplicada, Rio de Janeiro, Brasil. | Zbl | MR

[50] C.P. Gupta and L. Nachbin: Malgrange theorem for nuclearly entire functions on a Banach space. Preprint University of Rochester, Rochester, N.Y., (1968) U.S.A.

[51] M.C. Matos: Sur le théorème d'approximation et d'existence de Malgrange Gupta, C.R. Acad. Sci. Paris, 271 (1970), Ser. A, 1258-1259. | Zbl | MR

[52] M.C. Matos: Holomorphic mappings and domains of holomorphy. Monografias do Centro Brasileiro de Pesquisas Físicas, No. 27, Centro Brasileiro de Pesquisa Físicas, Rio de Janeiro (1970), Brasil. | Zbl

[53] M.C. Matos: On Malgrange Theorem for nuclear holomorphic functions in open balls of a Banach space. Math. Z. 162 (1978), 113-123. | Zbl | MR

[54] M.C. Matos: On convolution equations in a weak locally convex space. An. Acad. brasil. Cien. 49. (1977), 529-531. | Zbl | MR

[55] M.C. Matos: Convolution operators in spaces of uniform nuclear entire functions. To appear. | MR

[56] M.C. Matos and L. Nachbin: Silva-holomorphy types. Advances in Functional Analysis, Holomorphy and Approximation Theory (Editor: S. Machado). Lecture Notes in Math., Springer-Verlag. To appear. | Zbl | MR

[57] B. Malgrange: Existence et approximation des solutions des équations aux dérivées partielles et des équations des convolutions. Annales de L'Institut Fourier(Grenoble). VI (1955/6), 271-355. | Zbl | MR | Numdam

[58] A. Martineau: Sur les fonctionnelles analytiques et la transformation de Fourier Borel. Journal d'Analyse Mathématique. Vol. XI (1963), 1-164. | Zbl

[59] A. Martineau: Equations différentielles d'order infinie. Bull. Soc. Math. France, 95 (1967), 109-154. | Zbl | MR | Numdam

[60] L. Nachbin: Recent developments in infinite-dimensional holomorphy. Bull. Am. Math. Soc. 79 (1973), 625-640. | Zbl | MR

[61] L. Nachbin: Topology on spaces of holomorphic mappings. Ergebnisse der Mathematik und ihrer Grenzgebiet, Band 47. Springer-Verlag. Berlin (1969). | Zbl | MR

[62] L. Nachbin: Convolution operators in spaces of nuclearly entire functions on a Banach space. Functional Analysis and Related Fields (Editor: F.E. Browder Springer-Verlag, Berlin, (1970), 167-171. | Zbl

[63] L. Nachbin: Concerning holomorphy types for Banach spaces. Proc. International Colloquium on Nuclear Spaces and Ideals in Operator Algebras (Warsaw, 1969). Studia Math. 38 (1970), 407-412. | Zbl | MR

[64] L. Nachbin: Convoluções em funções inteiras nucleares. Atas da 2a Quinzema de Análise Funcional e Equações Diferenciais Parciais. Soc. Bras. de Matemática. (1972).

[65] B.A. Taylor: Some locally convex spaces of entire functions. Proceedings of Symposia in Pure Mathematics, Vol. 11. Entire Functions and Related Parts Analysis (1968), A.M.A. | Zbl