Entropy Numbers in Weighted Function Spaces and Eigenvalue Distributions of Some Degenerate Pseudodifferential Operators II

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 .