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.

Full Text

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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