Automorphisms of C commuting with partial integration operators in a rectangle
Banach Center Publications (2000)
- Volume: 53, Issue: 1, page 167-176
- ISSN: 0137-6934
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topMincheva, Svetlana. "Automorphisms of C commuting with partial integration operators in a rectangle." Banach Center Publications 53.1 (2000): 167-176. <http://eudml.org/doc/209071>.
@article{Mincheva2000,
abstract = {Convolutional representations of the commutant of the partial integration operators in the space of continuous functions in a rectangle are found. Necessary and sufficient conditions are obtained for two types of representing functions, to be the operators in the commutant continuous automorphisms. It is shown that these conditions are equivalent to the requirement that the considered representing functions be joint cyclic elements of the partial integration operators.},
author = {Mincheva, Svetlana},
journal = {Banach Center Publications},
keywords = {partial integration operators of the Volterra type; convolution operators; joint cyclic element},
language = {eng},
number = {1},
pages = {167-176},
title = {Automorphisms of C commuting with partial integration operators in a rectangle},
url = {http://eudml.org/doc/209071},
volume = {53},
year = {2000},
}
TY - JOUR
AU - Mincheva, Svetlana
TI - Automorphisms of C commuting with partial integration operators in a rectangle
JO - Banach Center Publications
PY - 2000
VL - 53
IS - 1
SP - 167
EP - 176
AB - Convolutional representations of the commutant of the partial integration operators in the space of continuous functions in a rectangle are found. Necessary and sufficient conditions are obtained for two types of representing functions, to be the operators in the commutant continuous automorphisms. It is shown that these conditions are equivalent to the requirement that the considered representing functions be joint cyclic elements of the partial integration operators.
LA - eng
KW - partial integration operators of the Volterra type; convolution operators; joint cyclic element
UR - http://eudml.org/doc/209071
ER -
References
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- [5] I. Dimovski, Convolutional Calculus, Kluwer Acad. Publ., Ser. 43, Dordrecht-Boston-London 1990. Zbl0685.44006
- [6] I. Dimovski and S. Mincheva, Automorphims of C which commute with the integration operator, Integral Transforms and Special Functions 4 (1996), 69-76. Zbl0862.45018
- [7] R. Edwards, Functional Analysis. Theory and Applications, New York 1965.
- [8] G. Fihtengolc, Cours of Differential and Integration Calculus, Vol. 2, FML, Moscow 1966, (in Russian).
- [9] R. Larsen, An Introduction to the Theory of Multipliers, Berlin - Heidelberg - New York 1972.
- [10] J. Mikusiński and C. Ryll-Nardzewski, Un théorème sur le produit de composition des fonctions de plusieurs variables, Studia Math. 13 (1953), 62-68. Zbl0050.10603
- [11] I. Raichinov, Linear operators defined in spaces of complex functions of many variables and commuting with the operators of integration, Serdica Bulg. Math. Publ. 4 (1978), 316-323. Zbl0437.47025
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