Hypercyclic convolution operators on entire functions of Hilbert-Schmidt holomorphy type

Henrik Petersson

Annales mathématiques Blaise Pascal (2001)

  • Volume: 8, Issue: 2, page 107-114
  • ISSN: 1259-1734

How to cite

top

Petersson, Henrik. "Hypercyclic convolution operators on entire functions of Hilbert-Schmidt holomorphy type." Annales mathématiques Blaise Pascal 8.2 (2001): 107-114. <http://eudml.org/doc/79231>.

@article{Petersson2001,
author = {Petersson, Henrik},
journal = {Annales mathématiques Blaise Pascal},
keywords = {exponential type; space of entire functions of Hilbert-Schmidt type; Hilbert space; continuous convolution operators; hypercyclic},
language = {eng},
number = {2},
pages = {107-114},
publisher = {Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal},
title = {Hypercyclic convolution operators on entire functions of Hilbert-Schmidt holomorphy type},
url = {http://eudml.org/doc/79231},
volume = {8},
year = {2001},
}

TY - JOUR
AU - Petersson, Henrik
TI - Hypercyclic convolution operators on entire functions of Hilbert-Schmidt holomorphy type
JO - Annales mathématiques Blaise Pascal
PY - 2001
PB - Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal
VL - 8
IS - 2
SP - 107
EP - 114
LA - eng
KW - exponential type; space of entire functions of Hilbert-Schmidt type; Hilbert space; continuous convolution operators; hypercyclic
UR - http://eudml.org/doc/79231
ER -

References

top
  1. [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. Zbl0938.47004MR1678318
  2. [2] G.D. Birkhoff. Démonstration d'un théoreme élémentaire sur les fonctions entières. C.R. Acad. Sci. Paris, 189:437-475, 1929. Zbl55.0192.07JFM55.0192.07
  3. [3] S. Dineen. Complex analysis on Infinite Dimensional Spaces. Springer-Verlag, 1999. Zbl1034.46504MR1705327
  4. [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. Zbl0222.46019MR290103
  5. [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. Zbl0618.30031MR884467
  6. [6] G. Godefroy and J.H. Shapiro. Operators with dense, invariant, cyclic vector manifolds. J. Funct. Anal., 98:229-269, 1991. MR 92d:47029. Zbl0732.47016MR1111569
  7. [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. Zbl0933.47003MR1685272
  8. [8] C. Gupta. Convolution operators and holomorphic mappings on a Banach space. Sem. Anal. Mod., No. 2, 1969. Univ. Sherbrooke. Québec. Zbl0243.47016
  9. [9] J. Horvath. Topological Vector Spaces and Distributions, volume 1. Addison-Wesley, Reading Massachusetts, 1966. Zbl0143.15101MR205028
  10. [10] C. Kitai. Invariant closed sets for linear operators. Ph.D. thesis, Univ. of Toronto, 1982. 
  11. [11] G.R. MacLane. Sequences of derivatives and normal families. J. Analyse Math., pages 72-87, 1952/53. MR 14:741d. Zbl0049.05603MR53231
  12. [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. Zbl0071.09002MR86990
  13. [13] H. Petersson. Fischer decompositions of entire functions of Hilbert-Schmidt holomorphy type. preprint and submitted, 2001. MR2066132
  14. [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. Zbl0782.47002MR959046
  15. [15] F. Treves. Linear partial differential equations with constant coefficients. Gordon and Breach, 1966. Zbl0164.40602MR224958

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.