Some properties of block-radial functions and Schrödinger type operators with block-radial potentials

Abstract

Let R γ B s p,q (R d ) be a subspace of the Besov space B s p,q (R d ) that consists of block-radial functions. We prove that the asymptotic behaviour of the entropy numbers of compact embeddings id :depends on the number of blocks of the lowest dimension, the parameters p 1 and p 2 , but is independent of the smoothness parameters s 1 , s 2 . We apply the asymptotic behaviour to estimation of powers of a negative spectra of Schrödinger type operators with block-radial potentials. This part essentially relies on the Birman-Schwinger principle.