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• W3104375864 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-Pruss Theorem for such spaces. We use the results to prove existence and uniqueness of solutions of a certain class of non-linear equations." @default.
• W3104375864 created "2020-11-23" @default.
• W3104375864 creator A5005129358 @default.
• W3104375864 creator A5026618511 @default.
• W3104375864 date "2015-09-22" @default.
• W3104375864 modified "2023-10-16" @default.
• W3104375864 title "Spectral Analysis of Abstract Parabolic Operators in Homogeneous Function Spaces" @default.
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• W3104375864 doi "https://doi.org/10.1007/s00009-015-0633-0" @default.
• W3104375864 hasPublicationYear "2015" @default.
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