Hypercyclic convolution operators on entire functions of Hilbert-Schmidt holomorphy type
Petersson, Henrik
Annales mathématiques Blaise Pascal, Tome 8 (2001), p. 107-114 / Harvested from Numdam
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@article{AMBP_2001__8_2_107_0,
     author = {Petersson, Henrik},
     title = {Hypercyclic convolution operators on entire functions of Hilbert-Schmidt holomorphy type},
     journal = {Annales math\'ematiques Blaise Pascal},
     volume = {8},
     year = {2001},
     pages = {107-114},
     mrnumber = {1888820},
     zbl = {01805816},
     zbl = {1024.47003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AMBP_2001__8_2_107_0}
}

Petersson, Henrik. Hypercyclic convolution operators on entire functions of Hilbert-Schmidt holomorphy type. Annales mathématiques Blaise Pascal, Tome 8 (2001) pp. 107-114. http://gdmltest.u-ga.fr/item/AMBP_2001__8_2_107_0/

[1] R. Aron and J. Bés. Hypercyclic differentiation operators. Function Spaces (Proc. Conf. Edwardsville, IL, 1998), Amer. Math. Soc. Providence, RI, pages 39-42, 1999. MR 2000b:47019. | MR 1678318 | Zbl 0938.47004

[2] G.D. Birkhoff. Démonstration d'un théoreme élémentaire sur les fonctions entières. C.R. Acad. Sci. Paris, 189:437-475, 1929. | JFM 55.0192.07

[3] S. Dineen. Complex analysis on Infinite Dimensional Spaces. Springer-Verlag, 1999. | MR 1705327 | Zbl 1034.46504

[4] A.W. Dwyer. Partial differential equations in Fischer-Fock spaces for the Hilbert-Schmidt holomorphy type. Bull. Amer. Soc., 77:725-730, 1971. MR 44#7288. | MR 290103 | Zbl 0222.46019

[5] R.M. Gethner and J.H. Shapiro. Universal vectors for operators on spaces of holomorphic functions. Proc. Amer. Math. Soc., No. 2, 100:281-288, 1987. MR 88g:47060. | MR 884467 | Zbl 0618.30031

[6] G. Godefroy and J.H. Shapiro. Operators with dense, invariant, cyclic vector manifolds. J. Funct. Anal., 98:229-269, 1991. MR 92d:47029. | MR 1111569 | Zbl 0732.47016

[7] K.-G. Grosse-Erdmann. Universal families and hypercyclic operators. Bull. Amer. Math. Soc. (N.S.). No. 3, 36:345-381, 1999. MR 2000c:47001. | MR 1685272 | Zbl 0933.47003

[8] C. Gupta. Convolution operators and holomorphic mappings on a Banach space. Sem. Anal. Mod., No. 2, 1969. Univ. Sherbrooke. Québec. | Zbl 0243.47016

[9] J. Horvath. Topological Vector Spaces and Distributions, volume 1. Addison-Wesley, Reading Massachusetts, 1966. | MR 205028 | Zbl 0143.15101

[10] C. Kitai. Invariant closed sets for linear operators. Ph.D. thesis, Univ. of Toronto, 1982.

[11] G.R. Maclane. Sequences of derivatives and normal families. J. Analyse Math., pages 72-87, 1952/53. MR 14:741d. | MR 53231 | Zbl 0049.05603

[12] B. Malgrange. Existence et approximation des solutions des équations aux dérivativées partielles et des équations de convolution. Ann. Inst. Fourier, 6:271-354, 1955. | Numdam | MR 86990 | Zbl 0071.09002

[13] H. Petersson. Fischer decompositions of entire functions of Hilbert-Schmidt holomorphy type. preprint and submitted, 2001. | MR 2066132 | Zbl 1088.46024

[14] C.J. Read. The invariant subspace problem for a class of Banach spaces. ii. Israel J. Math., 63:1-40, 1998. MR 90b:47013. | MR 959046 | Zbl 0782.47002

[15] F. Treves. Linear partial differential equations with constant coefficients. Gordon and Breach, 1966. | MR 224958 | Zbl 0164.40602