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arXiv · 1501.04958

Harmonic and Spectral Analysis of Abstract Parabolic Operators in Homogeneous Function Spaces

Anatoly G. Baskakov·Ilya A. Krishtal
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Abstract

We use methods of harmonic analysis and group representation theory to study the spectral properties of the abstract parabolic operator $\mathscr L = -d/dt+A$ in homogeneous function spaces. We provide sufficient conditions for invertibility of such operators in terms of the spectral properties of the operator $A$ and the semigroup generated by $A$. We introduce a homogeneous space of functions with absolutely summable spectrum and prove a generalization of the Gearhart-Prüss Theorem for such spaces. We use the results to prove existence and uniqueness of solutions of a certain class of non-linear equations.

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Anatoly G. Baskakov, Ilya A. Krishtal. 2015-01-20. Harmonic and Spectral Analysis of Abstract Parabolic Operators in Homogeneous Function Spaces. https://doi.org/10.1007/s00009-015-0633-0

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