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Joint functional calculus in algebra of polynomial tempered distributions


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.

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

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

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


@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 = {},


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