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# On the generation of Beurling type Carleman ultradifferentiable $C_0$-semigroups by scalar type spectral operators

### Abstract

A characterization of the scalar type spectral generators of Beurling type Carleman ultradifferentiable $C_0$-semigroups is established, the important case of the Gevrey ultradifferentiability is considered in detail, the implementation of the general criterion corresponding to a certain rapidly growing defining sequence is observed.

Key words: Scalar type spectral operator, $C_0$-semigroup of linear operators, Carleman classes of functions and vectors.

### Article Information

 Title On the generation of Beurling type Carleman ultradifferentiable $C_0$-semigroups by scalar type spectral operators Source Methods Funct. Anal. Topology, Vol. 22 (2016), no. 2, 169-183 MathSciNet MR3522858 zbMATH 06665386 Milestones Received 04/06/2015 Copyright The Author(s) 2016 (CC BY-SA)

### Authors Information

Marat V. Markin
Department of Mathematics, California State University, Fresno 5245 N. Backer Avenue, M/S PB 108 Fresno, CA 93740-8001

### Citation Example

Marat V. Markin, On the generation of Beurling type Carleman ultradifferentiable $C_0$-semigroups by scalar type spectral operators, Methods Funct. Anal. Topology 22 (2016), no. 2, 169-183.

### BibTex

@article {MFAT848,
AUTHOR = {Markin, Marat V.},
TITLE = {On the generation of Beurling type Carleman ultradifferentiable $C_0$-semigroups by scalar type spectral operators},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {22},
YEAR = {2016},
NUMBER = {2},
PAGES = {169-183},
ISSN = {1029-3531},
MRNUMBER = {MR3522858},
ZBLNUMBER = {06665386},
URL = {http://mfat.imath.kiev.ua/article/?id=848},
}

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