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Abstract:

A theorem of Godefroy and Shapiro states that non-trivial convolution operators on the space of entire functions on (Formula Presented.) are hypercyclic. Moreover, it was shown by Bonilla and Grosse-Erdmann that they have frequently hypercyclic functions of exponential growth. On the other hand, in the infinite dimensional setting, the Godefroy–Shapiro theorem has been extended to several spaces of entire functions defined on Banach spaces. We prove that on all these spaces, non-trivial convolution operators are strongly mixing with respect to a gaussian probability measure of full support. For the proof we combine the results previously mentioned and we use techniques recently developed by Bayart and Matheron. We also obtain the existence of frequently hypercyclic entire functions of exponential growth. © 2014, Springer Basel.

Registro:

Documento: Artículo
Título:Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions
Autor:Muro, S.; Pinasco, D.; Savransky, M.
Filiación:Departamento de Matemática-Pab I, Universidad de Buenos Aires, Ciudad Autónoma de Buenos Aires, 1428, Argentina
CONICET, Buenos Aires, Argentina
Departamento de Matemáticas y Estadística, UniversidadTorcuato di Tella, Av. F. Alcorta 7350, Ciudad Autónomade Buenos Aires, 1428, Argentina
Palabras clave:Convolution operators; Frequently hypercyclic operators; Holomorphy types; Strongly mixing operators
Año:2014
Volumen:80
Número:4
Página de inicio:453
Página de fin:468
DOI: http://dx.doi.org/10.1007/s00020-014-2182-5
Título revista:Integral Equations and Operator Theory
Título revista abreviado:Integr. Equ. Oper. Theory
ISSN:0378620X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0378620X_v80_n4_p453_Muro

Referencias:

  • Aron, R.M., Weakly uniformly continuous and weakly sequentially continuous entire functions (1979) Advances in Holomorphy (Proc. Sem. Univ. Fed. Rio de Janeiro, Rio de Janeiro, 1977). North-Holland Mathematics Studies, vol. 34, pp. 47-66. , North-Holland, Amsterdam:
  • Aron, R.M., Bés, J., Hypercyclic differentiation operators (1999) Function Spaces (Edwardsville, IL, 1998). Contemporary Mathematics, vol. 232, pp. 39-46. , American Mathematical Society, Providence:
  • Bayart, F., Grivaux, S., Hypercyclicity: the role of the unimodular point spectrum. (Hypercyclicité : Le rôle du spectre ponctuel unimodulaire) (2004) C. R. Math. Acad. Sci. Paris, 338 (9), pp. 703-708
  • Bayart, F., Matheron, É.: Mixing operators and small subsets of the circle. J. Reine Angew. Math. (2014, to appear); Bertoloto, F., Botelho, G., Fávaro, V., Jatobá, A., Hypercyclicity of convolution operators on spaces of entire functions (2013) Ann. Inst. Fourier, 63 (4), pp. 1263-1283
  • Blasco, O., Bonilla, A., Grosse-Erdmann, K.-G., Rate of growth of frequently hypercyclic functions (2010) Proc. Edinb. Math. Soc. (2), 53 (1), pp. 39-59
  • Bonilla, A., Grosse-Erdmann, K.-G., On a theorem of Godefroy and Shapiro (2006) Integral Equ. Oper. Theory, 56 (2), pp. 151-162
  • Bonilla, A., Grosse-Erdmann, K.-G., Frequently hypercyclic subspaces (2012) Monatsh. Math, 168 (3-4), pp. 305-320
  • Carando, D., Extendibility of polynomials and analytic functions on l p (2001) Studia Math, 145 (1), pp. 63-73
  • Carando, D., Dimant, V., Muro, S., Hypercyclic convolution operators on Fréchet spaces of analytic functions (2007) J. Math. Anal. Appl, 336 (2), pp. 1324-1340
  • Carando, D., Dimant, V., Muro, S., Holomorphic Functions and polynomial ideals on Banach spaces (2012) Collect. Math, 63 (1), pp. 71-91
  • Carando, D., Galicer, D., The symmetric Radon–Nikodym property for tensor norms (2011) J. Math. Anal. Appl, 375 (2), pp. 553-565
  • Dimant, V., Galindo, P., Maestre, M., Zalduendo, I., Integral holomorphic functions (2004) Studia Math, 160 (1), pp. 83-99
  • Dineen, S., Holomorphy types on a Banach space (1971) Studia Math, 39, pp. 241-288
  • Dineen, S., (1999) Complex analysis on infinite dimensional spaces. Springer Monographs in Mathematics, , Springer, London:
  • Duyos-Ruiz, S.M., On the existence of universal functions (1983) Dokl. Akad. Nauk SSSR, 268 (1), pp. 18-22
  • Dwyer, T.A.W.I.I.I., Partial differential equations in Fischer-Fock spaces for the Hilbert–Schmidt holomorphy type (1971) Bull. Am. Math. Soc, 77, pp. 725-730
  • Fávaro, V., Jatobá, A.M., Holomorphy types and spaces of entire functions of bounded type on Banach spaces (2009) Czech. Math. J, 59 (4), pp. 909-927
  • Floret, K., Minimal ideals of n-homogeneous polynomials on Banach spaces (2001) Result. Math, 39 (3-4), pp. 201-217
  • Floret, K., On ideals of n-homogeneous polynomials on Banach spaces (2002) Topological Algebras with Applications to Differential Geometry and Mathematical Physics (Athens, 1999), pp. 19-38. , Univ. Athens, Athens:
  • Godefroy, G., Shapiro, J.H., Operators with dense, invariant, cyclic vector manifolds (1991) J. Funct. Anal, 98 (2), pp. 229-269
  • Grosse-Erdmann, K.-G., On the universal functions of G. R. MacLane (1990) Complex Var. Theory Appl, 15 (3), pp. 193-196
  • Grosse-Erdmann, K.-G., Peris Manguillot, A., (2011) Linear chaos, xii, 386 p. Universitext, , Springer, Berlin:
  • Gupta, C.P., On the Malgrange theorem for nuclearly entire functions of bounded type on a Banach space (1970) Nederl. Akad. Wetensch. Proc. Ser. A73 Indag. Math, 32, pp. 356-358
  • Muro, S., On algebras of holomorphic functions of a given type (2012) J. Math. Anal. Appl, 389 (2), pp. 792-811
  • Nachbin, L., (1969) Topology on spaces of holomorphic mappings. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 47, , Springer, New York:
  • Petersson, H., Hypercyclic convolution operators on entire functions of Hilbert–Schmidt holomorphy type (2001) Ann. Math. Blaise Pascal, 8 (2), pp. 107-114
  • Petersson, H., Hypercyclic subspaces for Fréchet space operators (2006) J. Math. Anal. Appl, 319 (2), pp. 764-782
  • Shkarin, S.A., On the growth of D-universal functions. Vestnik Moskov. Univ. Ser. I Mat (1993) Mekh. 48(6), 80-83 (1994)

Citas:

---------- APA ----------
Muro, S., Pinasco, D. & Savransky, M. (2014) . Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions. Integral Equations and Operator Theory, 80(4), 453-468.
http://dx.doi.org/10.1007/s00020-014-2182-5
---------- CHICAGO ----------
Muro, S., Pinasco, D., Savransky, M. "Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions" . Integral Equations and Operator Theory 80, no. 4 (2014) : 453-468.
http://dx.doi.org/10.1007/s00020-014-2182-5
---------- MLA ----------
Muro, S., Pinasco, D., Savransky, M. "Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions" . Integral Equations and Operator Theory, vol. 80, no. 4, 2014, pp. 453-468.
http://dx.doi.org/10.1007/s00020-014-2182-5
---------- VANCOUVER ----------
Muro, S., Pinasco, D., Savransky, M. Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions. Integr. Equ. Oper. Theory. 2014;80(4):453-468.
http://dx.doi.org/10.1007/s00020-014-2182-5