Open AccessOn the asymptotic eigenvalue distribution of a pseudo-differential operator
Author(s) -
Charles Fefferman,
D. H. Phong
Publication year - 1980
Publication title -
proceedings of the national academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.77.10.5622
Subject(s) - differential operator , eigenvalues and eigenvectors , mathematics , symbol (formal) , operator (biology) , distribution (mathematics) , differential (mechanical device) , combinatorics , symbol of a differential operator , mathematical analysis , unit (ring theory) , pure mathematics , physics , differential equation , quantum mechanics , computer science , chemistry , ordinary differential equation , thermodynamics , transcription factor , repressor , differential algebraic equation , biochemistry , gene , programming language , mathematics education
A description of the number N(K) of eigenvalues less than K for a pseudo-differential operator with positive symbol is given in terms of the number of unit cubes canonically imbedded in the subset of phase space where the symbol is less than CK. This gives back in particular the order of magnitude of N(K) for elliptic symbols.
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