Accurate Spectral Asymptotics for periodic operators | Zendy

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Accurate Spectral Asymptotics for periodic operators

Author(s) -

Victor Ivrii

Publication year - 1999

Publication title -

journées équations aux dérivées partielles

Language(s) - English

Resource type - Journals

eISSN - 2118-9366

pISSN - 0752-0360

DOI - 10.5802/jedp.549

Subject(s) - eigenvalues and eigenvectors , operator (biology) , remainder , infinity , matrix (chemical analysis) , mathematics , spectral properties , mathematical analysis , pure mathematics , combinatorics , physics , arithmetic , quantum mechanics , materials science , chemistry , composite material , astrophysics , biochemistry , repressor , transcription factor , gene

Asymptotics with sharp remainder estimates are recovered for number N( ) of eigenvalues of operator A(x,D) tW(x,x) crossing level E as t runs from 0 to , ! 1. Here A is periodic matrix operator, matrix W is positive, periodic with respect to first copy of x and decaying as second copy of x goes to infinity, E either belongs to a spectral gap of A or is one its ends. These problems are first treated in papers of M.Sh.Birman, M.Sh.Birman-A.Laptev and M.Sh.Birman-T.Suslina.

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