Characterization of the Gamma semigroup

Shmuel Kantorovitz

doi:10.1007/s00233-016-9787-8

Characterization of the Gamma semigroup

Shmuel Kantorovitz

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The Gamma semigroup with parameter b> 0 on L^p(R⁺) is defined by (Formula Presented.).Let S denote the multiplication operator f(x) → xf(x) with maximal domain D(S) in L^p(R⁺). The bounded operator V on L^p(R⁺) is S-Volterra if D(S) is V-invariant and [ S, V] = V² on D(S). For 1 < p< ∞, we characterize the Gamma semigroup as the unique regular semigroup V(· ) on L^p(R⁺) with imaginary type less than π, such that V(1) is S-Volterra and V(1 ) u^b= Su^b, where u^b(x) : = e^- ^b ^x.

Original language	English
Pages (from-to)	251-258
Number of pages	8
Journal	Semigroup Forum
Volume	95
Issue number	2
DOIs	https://doi.org/10.1007/s00233-016-9787-8
State	Published - 1 Oct 2017

Bibliographical note

Publisher Copyright:
© 2016, Springer Science+Business Media New York.

Keywords

Gamma semigroup
Imaginary type
Regular semigroup
S-Volterra operator

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10.1007/s00233-016-9787-8

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Characterization of the Gamma semigroup

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Keywords

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