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# Joint functional calculus in algebra of polynomial tempered distributions

### Abstract

In this paper we develop a functional calculus for a countable system of generators of contraction strongly continuous semigroups. As a symbol class of such calculus we use the algebra of polynomial tempered distributions. We prove a differential property of constructed calculus and describe its image with the help of the commutant of polynomial shift semigroup. As an application, we consider a function of countable set of second derivative operators.

Key words: Functional calculus for generators of operator semigroups, polynomials on locally convex spaces, infinite parameter operator semigroups.

### Article Information

 Title Joint functional calculus in algebra of polynomial tempered distributions Source Methods Funct. Anal. Topology, Vol. 22 (2016), no. 1, 62-73 MathSciNet MR3522862 zbMATH 06630283 Milestones Received 29/12/2014; Revised 21/04/2015 Copyright The Author(s) 2016 (CC BY-SA)

### Authors Information

S. V. Sharyn
Department of Mathematics and Computer Sciences, Precarpathian National University, 57 Shevchenka str., Ivano-Frankivsk, 76018, Ukraine

### Citation Example

S. V. Sharyn, Joint functional calculus in algebra of polynomial tempered distributions, Methods Funct. Anal. Topology 22 (2016), no. 1, 62-73.

### BibTex

@article {MFAT845,
AUTHOR = {Sharyn, S. V.},
TITLE = {Joint functional calculus in algebra of polynomial tempered distributions},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {22},
YEAR = {2016},
NUMBER = {1},
PAGES = {62-73},
ISSN = {1029-3531},
MRNUMBER = {MR3522862},
ZBLNUMBER = {06630283},
URL = {http://mfat.imath.kiev.ua/article/?id=845},
}

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