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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)