About nilpotent $C_0$-semigroups of operators in the Hilbert spaces and criteria for similarity to the integration operator

Abstract

In the paper, we describe a class of operators $A$ that have empty spectrum and satisfy the nilpotency property of the generated $C_0$-semigroup $U(t)=\exp\{-iAt\},\, t\geqslant 0$, and such that the operator$A^{-1}$ is similar to the integration operator on the corresponding space $L_2(0,a)$.

Full Text

Article Information

Title	About nilpotent $C_0$-semigroups of operators in the Hilbert spaces and criteria for similarity to the integration operator
Source	Methods Funct. Anal. Topology, Vol. 14 (2008), no. 1, 60-66
MathSciNet	MR2402153
Copyright	The Author(s) 2008 (CC BY-SA)

Authors Information

G. V. Lukashenko
Poltava National Technical University, 24 Pervomaiskii prospect, Poltava, 36011, Ukraine

G. M. Gubreev
Poltava National Technical University, 24 Pervomaiskii prospect, Poltava, 36011, Ukraine

 

Citation Example

G. V. Lukashenko and G. M. Gubreev, About nilpotent $C_0$-semigroups of operators in the Hilbert spaces and criteria for similarity to the integration operator, Methods Funct. Anal. Topology 14 (2008), no. 1, 60-66.

BibTex

@article {MFAT444,
    AUTHOR = {Lukashenko, G. V. and Gubreev, G. M.},
     TITLE = {About nilpotent $C_0$-semigroups of operators in the Hilbert spaces and criteria for similarity to the integration operator},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {14},
      YEAR = {2008},
    NUMBER = {1},
     PAGES = {60-66},
      ISSN = {1029-3531},
  MRNUMBER = {MR2402153},
       URL = {http://mfat.imath.kiev.ua/article/?id=444},
}