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Upper semi-Fredholm and Kato spectrum of an $\alpha$-times integrated semigroup

Abstract

Let $(T(t))_{t\geq 0}$ be an $\alpha$-times integrated semigroup with generator $A$ on a Banach space $X$. In this paper, we show that the spectral mapping theorem holds for upper semi-Fredholm spectrum and we will give some consequences of this result. We also give an application on the Schrödinger operator.

Key words: $\alpha$-times integrated semigroup, upper semi-Fredholm, Kato, essentially Kato, SVEP

Article Information

 Title Upper semi-Fredholm and Kato spectrum of an $\alpha$-times integrated semigroup Source Methods Funct. Anal. Topology, Vol. 26 (2020), no. 1, 63-67 Milestones Received 06/09/2019; Revised 12/10/201 Copyright The Author(s) 2020 (CC BY-SA)

Hamid Boua

Citation Example

Hamid Boua, Upper semi-Fredholm and Kato spectrum of an $\alpha$-times integrated semigroup, Methods Funct. Anal. Topology 26 (2020), no. 1, 63-67.

BibTex

@article {MFAT1288,
AUTHOR = {Hamid Boua},
TITLE = {Upper semi-Fredholm and Kato spectrum of an  $\alpha$-times integrated
semigroup},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {26},
YEAR = {2020},
NUMBER = {1},
PAGES = {63-67},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=1288},
}

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