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Spectral Asymptotics for Sturm‐Liouville Equations
Author(s) -
Bennewits C.
Publication year - 1989
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/plms/s3-59.2.294
Subject(s) - mathematics , mathematical analysis , function (biology) , eigenvalues and eigenvectors , spectral function , spectral radius , radius , order (exchange) , distribution (mathematics) , pure mathematics , physics , computer security , finance , quantum mechanics , evolutionary biology , computer science , economics , biology , condensed matter physics
The basis results of this paper giver asymptotic formulas and order of magnitude estimates for the socalled Titchmarsh‐Weyl m ‐function of the equation (0.2) which are valid also for quite irregular coefficients. As a consequence asymptotic results are obtained for many other spectral quantities, e.g. the eigen‐value distribution, Green's function, the spectral function and the integral kernels of the spectral projectors. A formula for the radius of the ‘Weyl disk’ is also given. The classical ‘right‐definite’ case is considered as well as the ‘left‐definite’ case.