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Entropy Numbers in Weighted Function Spaces and Eigenvalue Distributions of Some Degenerate Pseudodifferential Operators II
Author(s) -
Haroske Dorothee,
Triebel Hans
Publication year - 1994
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19941680108
Subject(s) - pseudodifferential operators , mathematics , degenerate energy levels , eigenvalues and eigenvectors , pure mathematics , type (biology) , function (biology) , mathematical analysis , quantum mechanics , physics , ecology , evolutionary biology , biology
This paper is the continuation of [17]. We investigate mapping and spectral properties of pseudodifferential operators of type Ψ 1, γ xwith χ χ ϵ ℝ and 0 ≤ γ ≤ 1 in the weighted function spaces B p,q s(ℝ n , w(x )) and F p,q s(ℝ n , w(x )) treated in [17]. Furthermore, we study the distribution of eigenvalues and the behaviour of corresponding root spaces for degenerate pseudodifferential operators preferably of type b 2 ( x ) b ( x, D ) b 1 ( x ), where b 1 ( x ) and b 2 ( x ) are appropriate functions and b(x, D ) ϵ Ψ 1, γ x . Finally, on the basis of the Birman‐Schwinger principle, we deal with the “negative spectrum” (bound states) of related symmetric operators in L 2 .