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On the resolvent arising in a parameter‐elliptic multi‐order boundary problem
Author(s) -
Faierman M.
Publication year - 2012
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.201000157
Subject(s) - mathematics , resolvent , boundary (topology) , boundary value problem , hilbert space , bounded function , mathematical analysis , elliptic operator , eigenvalues and eigenvectors , robin boundary condition , differential operator , smoothness , pure mathematics , mixed boundary condition , physics , quantum mechanics
In this paper we consider a boundary problem for a parameter‐elliptic, multi‐order system of differential equations defined over a bounded region in \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb {R}^n$\end{document} and under limited smoothness assumptions as well as under boundary conditions which include those of Dirichlet. Information is then derived concerning the asymptotic behaviour of the trace of a power of the resolvent of the Hilbert space operator, in general non‐selfadjoint, induced by the boundary problem under null boundary conditions. This information will then be used in a subsequent work to derive various results pertaining to the asymptotic behaviour of the eigenvalues of this operator.