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On the Eigenvalue Problem for a Certain
Author(s) -
Babarsky Richard,
Wood Houston G.
Publication year - 1986
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1986753249
Subject(s) - eigenvalues and eigenvectors , mathematics , resolvent , operator (biology) , perturbation (astronomy) , mathematical analysis , semi elliptic operator , differential operator , domain (mathematical analysis) , partial differential equation , pure mathematics , physics , quantum mechanics , biochemistry , repressor , transcription factor , gene , chemistry
This paper studies the spectral properties of the partial differential operator over a finite region Ω. This operator, which arises in the analysis of nonaxisymmetric, rapidly rotating compressible flows, is treated as a perturbation of the operator which is generated by the terms Using the fact that , when defined on a suitable domain, is closed and self‐adjoint, it is shown that [when acting on elements of ] is an operator with compact resolvent whose generalized eigenvectors are complete in ℒ 2 (Ω).