Entire functions on locally convex spaces and convolution operators
Matos, Mario C. ; Nachbin, Leopoldo
Compositio Mathematica, Tome 44 (1981), p. 145-181 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1981-01-01
@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},
     volume = {44},
     year = {1981},
     pages = {145-181},
     mrnumber = {662461},
     zbl = {0485.46022},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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) pp. 145-181. http://gdmltest.u-ga.fr/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. | MR 341088 | Zbl 0226.46018

[2] R. Aron: Tensor products of holomorphic functions, Nederl. Akad. Wetensch. Indag. Math. 35 (76) (1973), Fasc. 3, 192-202. | MR 346530 | Zbl 0261.46031

[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. | MR 520652 | Zbl 0404.46024

[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. | MR 201959 | Zbl 0149.09601

[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). | MR 202392 | Zbl 0151.44001

[6] P. Berner: Convolution operators and surjective limits. Advances in Holomorphy (Editor J.A. Barroso) North-Holland Publishing Co. (1979), 93-102. | MR 520656 | Zbl 0416.46031

[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. | MR 407598 | Zbl 0243.46038

[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 0323.46043

[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. | MR 420271 | Zbl 0282.46019

[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. | MR 394201 | Zbl 0314.46045

[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 493331

[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. | MR 407599 | Zbl 0247.46043

[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. | MR 599017 | Zbl 0441.46037

[16] J.F. Colombeau: Differentiable mappings on real nuclear Silva spaces and applications. To appear in Revue Roumaine de Math. Pures et Appliquées. | MR 577187 | Zbl 0494.46043

[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. | MR 520661 | Zbl 0446.46037

[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. | MR 554328 | Zbl 0426.46015

[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. | MR 433207 | Zbl 0349.46042

[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. | MR 433208 | Zbl 0361.46035

[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. | MR 520663 | Zbl 0479.46032

[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. | MR 442680 | Zbl 0357.46051

[23] J.F. Colombeau and B. Perrot: The Fourier-Borel transform in infinitely many dimensions and applications. To appear. | MR 610829 | Zbl 0476.46045

[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 0433.46040

[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. | MR 597996 | Zbl 0453.46033

[27] J.F. Colombeau and M.C. Matos: On some spaces of entire functions defined on infinite dimensional spaces. To appear. | MR 634762 | Zbl 0483.46018

[28] J.F. Colombeau and B. Perrot: Reflexivity and kernels in infinite dimensional holomorphic. To appear in Portugaliae Mathematica. | MR 597851 | Zbl 0441.46021

[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. | MR 606696 | Zbl 0453.46034

[31] S. Dineen: Holomorphic functions on a Banach space. Bull. Amer. Math. Soc. 76 (1970), 883-886. | MR 259578 | Zbl 0237.46027

[32] S. Dineen: Holomorphic types on a Banach space. Studia Math. 39 (1971), 241-288. | MR 304705 | Zbl 0235.32013

[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. | MR 487451 | Zbl 0328.46047

[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. | MR 487450 | Zbl 0299.46036

[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. | MR 482181 | Zbl 0377.46061

[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. | MR 320749 | Zbl 0271.35064

[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. | MR 290103 | Zbl 0222.46019

[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. | MR 402496 | Zbl 0327.46048

[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. | MR 404893 | Zbl 0308.46043

[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. | MR 383077 | Zbl 0308.46042

[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 0319.46032

[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. | Numdam | MR 482192 | Zbl 0331.46039

[43] T.A.W. Dwyer Iii.: Infinite Dimensional Analytic Systems. Proceedings of the 1977, IEEE Conference on Decision and Control (1977), 285-290. | MR 504200

[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. | MR 482180 | Zbl 0441.46034

[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. | MR 479504 | Zbl 0372.93024

[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). | MR 502427 | Zbl 0386.35022

[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. | MR 290104 | Zbl 0201.44605

[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 0243.47016

[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. | MR 632066 | Zbl 0182.45402

[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. | MR 285888 | Zbl 0205.40902

[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 0233.32004

[53] M.C. Matos: On Malgrange Theorem for nuclear holomorphic functions in open balls of a Banach space. Math. Z. 162 (1978), 113-123. | MR 632054 | Zbl 0402.46029

[54] M.C. Matos: On convolution equations in a weak locally convex space. An. Acad. brasil. Cien. 49. (1977), 529-531. | MR 493335 | Zbl 0377.47035

[55] M.C. Matos: Convolution operators in spaces of uniform nuclear entire functions. To appear. | MR 687994

[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. | MR 610841 | Zbl 0484.46045

[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. | Numdam | MR 86990 | Zbl 0071.09002

[58] A. Martineau: Sur les fonctionnelles analytiques et la transformation de Fourier Borel. Journal d'Analyse Mathématique. Vol. XI (1963), 1-164. | Zbl 0124.31804

[59] A. Martineau: Equations différentielles d'order infinie. Bull. Soc. Math. France, 95 (1967), 109-154. | Numdam | MR 1507968 | Zbl 0167.44202

[60] L. Nachbin: Recent developments in infinite-dimensional holomorphy. Bull. Am. Math. Soc. 79 (1973), 625-640. | MR 322509 | Zbl 0279.32017

[61] L. Nachbin: Topology on spaces of holomorphic mappings. Ergebnisse der Mathematik und ihrer Grenzgebiet, Band 47. Springer-Verlag. Berlin (1969). | MR 254579 | Zbl 0172.39902

[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 0217.16403

[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. | MR 278055 | Zbl 0212.14701

[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 0181.13304