Fundamental solutions and mapping properties of semielliptic operators | Zendy

Hile G. N. | Zendy

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Fundamental solutions and mapping properties of semielliptic operators

Author(s) -

Hile G. N.

Publication year - 2006

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200410436

Subject(s) - mathematics , isomorphism (crystallography) , pure mathematics , class (philosophy) , elliptic operator , function (biology) , algebra over a field , mathematical analysis , computer science , chemistry , artificial intelligence , evolutionary biology , crystal structure , biology , crystallography

An explicit formula is given for a fundamental solution for a class of semielliptic operators. The fundamental solution is used to investigate properties of these operators as mappings between weighted function spaces in ℝ n . Necessary and sufficient conditions are given for such a mapping to be an isomorphism. Results apply, for example, to elliptic, parabolic, and generalized p ‐parabolic operators. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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