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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 27, Issue 5


Separable convolution-elliptic operators with parameters

Veli B. Shakhmurov
  • Department of Mechanical Engineering, Okan University, Akfirat Beldesi, Tuzla, 34959, Istanbul, Turkey; and Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Azerbaijan
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Published Online: 2013-11-23 | DOI: https://doi.org/10.1515/forum-2013-0101


The maximal regularity properties of parameter dependent abstract convolution-elliptic equations are investigated. Here find sufficient conditions that guarantee the uniform separability of these problems in Lp spaces. It is established that the corresponding convolution-elliptic operator is sectorial and is also a generator of an analytic semigroup. Finally, these results applied to obtain the uniform maximal regularity for the Cauchy problem for abstract parabolic equation in mixed L𝐩 norms, boundary value problems for anisotropic integro-differential equations and infinite systems of elliptic integro-differential equations with parameters.

Keywords: Sectorial operators; Banach-valued spaces; operator-valued multipliers; boundary value problems with parameters; convolution equations; integro-differential equations

MSC: 34G10; 45J05; 45K05

About the article

Received: 2013-06-12

Published Online: 2013-11-23

Published in Print: 2015-09-01

Citation Information: Forum Mathematicum, Volume 27, Issue 5, Pages 2637–2660, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2013-0101.

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