# 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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- [2] N. Bozhinov, Operational calculus for partial differential operators of first and second order, in: Math. and Math. Educ. - 1978, Sofia, 1978, 231-240, (in Bulgarian).
- [3] N. Bozhinov and I. Dimovski, Convolutions, multipliers and commutants related to double complex Dirichlet expansions, Pliska Stud. Math. Bulg. 4 (1981), 117-127.
- [4] N. Bozhinov and I. Dimovski, Convolutions, multipliers and commutants related to multiple complex Dirichlet expansions, Serdica Bulg. Math. Publ. 9 (1983), 172-188.
- [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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