In this paper we use Nachbin’s holomorphy types to generalize some recent results concerning hypercyclic convolution operators on Fréchet spaces of entire functions of bounded type of infinitely many complex variables
Dans cet article, nous utilisons les types d’holomorphie de Nachbin pour généraliser certains résultats récents concernant les opérateurs de convolutions hypercycliques sur les espaces de Fréchet de fonctions d’un nombre infini de variables complexes, entières, de type borné.
Keywords: Fréchet spaces of entire functions, hypercyclicity, convolution operators
Mot clés : Espaces de Fréchet de fonctions entières, hypercyclicité, opérateurs de convolution
@article{AIF_2013__63_4_1263_0, author = {Bertoloto, F.J. and Botelho, G. and F\'avaro, V.V. and Jatob\'a, A.M.}, title = {Hypercyclicity of convolution operators on spaces of entire functions}, journal = {Annales de l'Institut Fourier}, pages = {1263--1283}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {63}, number = {4}, year = {2013}, doi = {10.5802/aif.2803}, zbl = {1300.32010}, mrnumber = {3137355}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2803/} }
TY - JOUR AU - Bertoloto, F.J. AU - Botelho, G. AU - Fávaro, V.V. AU - Jatobá, A.M. TI - Hypercyclicity of convolution operators on spaces of entire functions JO - Annales de l'Institut Fourier PY - 2013 SP - 1263 EP - 1283 VL - 63 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2803/ DO - 10.5802/aif.2803 LA - en ID - AIF_2013__63_4_1263_0 ER -
%0 Journal Article %A Bertoloto, F.J. %A Botelho, G. %A Fávaro, V.V. %A Jatobá, A.M. %T Hypercyclicity of convolution operators on spaces of entire functions %J Annales de l'Institut Fourier %D 2013 %P 1263-1283 %V 63 %N 4 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2803/ %R 10.5802/aif.2803 %G en %F AIF_2013__63_4_1263_0
Bertoloto, F.J.; Botelho, G.; Fávaro, V.V.; Jatobá, A.M. Hypercyclicity of convolution operators on spaces of entire functions. Annales de l'Institut Fourier, Volume 63 (2013) no. 4, pp. 1263-1283. doi : 10.5802/aif.2803. http://www.numdam.org/articles/10.5802/aif.2803/
[1] Hypercyclic differentiation operators, Function spaces (Edwardsville, IL, 1998) (Contemp. Math.), Volume 232, Amer. Math. Soc., Providence, RI, 1999, pp. 39-46 | DOI | MR | Zbl
[2] On universal functions, J. Korean Math. Soc., Volume 41 (2004) no. 1, pp. 65-76 (Satellite Conference on Infinite Dimensional Function Theory) | DOI | MR | Zbl
[3] Démonstration d’un théorème élémentaire sur les fonctions entières, C. R. Acad. Sci. Paris, Volume 189 (1929), pp. 473-475
[4] Holomorphy types and ideals of multilinear mappings, Studia Math., Volume 177 (2006) no. 1, pp. 43-65 | DOI | MR | Zbl
[5] Two new properties of ideals of polynomials and applications, Indag. Math. (N.S.), Volume 16 (2005) no. 2, pp. 157-169 | DOI | MR | Zbl
[6] Hypercyclic convolution operators on Fréchet spaces of analytic functions, J. Math. Anal. Appl., Volume 336 (2007) no. 2, pp. 1324-1340 | DOI | MR | Zbl
[7] Coherent sequences of polynomial ideals on Banach spaces, Math. Nachr., Volume 282 (2009) no. 8, pp. 1111-1133 | DOI | MR | Zbl
[8] Every Banach ideal of polynomials is compatible with an operator ideal, Monatsh. Math., Volume 165 (2012) no. 1, pp. 1-14 | DOI | MR | Zbl
[9] Complex analysis on infinite-dimensional spaces, Springer Monographs in Mathematics, Springer-Verlag London Ltd., London, 1999 | DOI | MR | Zbl
[10] Convolution equations on spaces of quasi-nuclear functions of a given type and order, Bull. Belg. Math. Soc. Simon Stevin, Volume 17 (2010) no. 3, pp. 535-569 http://projecteuclid.org/getRecord?id=euclid.bbms/1284570737 | MR | Zbl
[11] Holomorphy types and spaces of entire functions of bounded type on Banach spaces, Czechoslovak Math. J., Volume 59(134) (2009) no. 4, pp. 909-927 | DOI | MR | Zbl
[12] Sierpiński-Zygmund functions and other problems on lineability, Proc. Amer. Math. Soc., Volume 138 (2010) no. 11, pp. 3863-3876 | DOI | MR | Zbl
[13] Universal vectors for operators on spaces of holomorphic functions, Proc. Amer. Math. Soc., Volume 100 (1987) no. 2, pp. 281-288 | DOI | MR | Zbl
[14] Operators with dense, invariant, cyclic vector manifolds, J. Funct. Anal., Volume 98 (1991) no. 2, pp. 229-269 | DOI | MR | Zbl
[15] Convolution operators and holomorphic mappings on a Banach space, Séminaire d’Analyse Moderne, No. 2, Dept. Math, Université de Sherbrooke, Québec, 1969 | Zbl
[16] On the Malgrange theorem for nuclearly entire functions of bounded type on a Banach space, Nederl. Akad. Wetensch. Proc. Ser. A73 = Indag. Math., Volume 32 (1970), pp. 356-358 | DOI | MR | Zbl
[17] Hypercyclicity for translations through Runge’s theorem, Bull. Korean Math. Soc., Volume 44 (2007) no. 1, pp. 117-123 | DOI | MR | Zbl
[18] Invariant closed sets for linear operators, ProQuest LLC, Ann Arbor, MI, 1982 Thesis (Ph.D.)–University of Toronto (Canada) | MR
[19] Sequences of derivatives and normal families, J. Analyse Math., Volume 2 (1952), pp. 72-87 | DOI | MR | Zbl
[20] Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution, Ann. Inst. Fourier, Grenoble, Volume 6 (1955–1956), pp. 271-355 | DOI | Numdam | MR | Zbl
[21] Mappings between Banach spaces that send mixed summable sequences into absolutely summable sequences, J. Math. Anal. Appl., Volume 297 (2004) no. 2, pp. 833-851 (Special issue dedicated to John Horváth) | DOI | MR | Zbl
[22] Absolutely Summing Mappings, Nuclear Mappings and Convolution Equations, IMECC-UNICAMP, 2005 (http://www.ime.unicamp.br/rel_pesq/2007/pdf/rp03-07.pdf)
[23] Complex analysis in Banach spaces, North-Holland Mathematics Studies, 120, North-Holland Publishing Co., Amsterdam, 1986 | MR | Zbl
[24] Aplicações -somantes e -nucleares, Universidade Estadual de Campinas (2006) (Ph. D. Thesis http://cutter.unicamp.br/document/?code =vtls000378266)
[25] Topology on spaces of holomorphic mappings, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 47, Springer-Verlag New York Inc., New York, 1969 | MR | Zbl
[26] Hypercyclic convolution operators on entire functions of Hilbert-Schmidt holomorphy type, Ann. Math. Blaise Pascal, Volume 8 (2001) no. 2, pp. 107-114 | DOI | Numdam | MR | Zbl
[27] Hypercyclic subspaces for Fréchet space operators, J. Math. Anal. Appl., Volume 319 (2006) no. 2, pp. 764-782 | DOI | MR | Zbl
Cited by Sources: