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1998 | 130 | 1 | 23-52
Tytuł artykułu

On p-dependent local spectral properties of certain linear differential operators in $L^{p}(ℝ^{N})

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The aim is to investigate certain spectral properties, such as decomposability, the spectral mapping property and the Lyubich-Matsaev property, for linear differential operators with constant coefficients ( and more general Fourier multiplier operators) acting in $L^p(ℝ^N)$. The criteria developed for such operators are quite general and p-dependent, i.e. they hold for a range of p in an interval about 2 (which is typically not (1,∞)). The main idea is to construct appropriate functional calculi: this is achieved via a combination of methods from the theory of Fourier multipliers and local spectral theory.
Słowa kluczowe
  • Fachbereich Mathematik, Universität des Saarlandes, Postfach 151150, D-66141 Saarbrücken, Germany
  • School of Mathematics, University of New South Wales, Sydney, N.S.W., 2025, Australia
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