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Spectral Asymptotics for Higher‐Order Ordinary Differential Equations
Author(s) -
Bennewitz C,
Wood AD
Publication year - 1997
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611597000208
Subject(s) - mathematics , ordinary differential equation , reciprocal , interval (graph theory) , mathematical analysis , function (biology) , pure mathematics , mathematics subject classification , order (exchange) , differential equation , combinatorics , philosophy , linguistics , finance , evolutionary biology , economics , biology
This paper gives one‐term componentwise asymptotics for the M and spectral matrices of a self‐adjoint realisation of an even‐order ordinary differential expression. The underlying interval is assumed to have at least one regular endpoint, and the boundary conditions are supposed to be separated. Furthermore, the weight function and the reciprocal of the highest‐order coefficient are supposed to be of regular variation at the regular endpoint, in the sense of Bingham, Goldie and Teugels. 1991 Mathematics Subject Classification : 34B24, 34E05.