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Some properties of block-radial functions and Schr\"odinger type operators with block-radial potentials by Dota, Alicja; Skrzypczak, Leszek is a scholarly article available to read on EtoBox.

What is Some properties of block-radial functions and Schr\"odinger type operators with block-radial potentials about?

Let $ R_\gamma B^{s}_{p,q}(\Rd)$ be a subspace of the Besov space $B^{s}_{p,q}(\Rd)$ that consists of block-radial functions. We prove that the asymptotic behaviour of the entropy numbers of compact embeddings $\id: \: R_\gamma B^{s_1}_{p_1,q_1}(\R^d) \rightarrow R_\gamma B^{s_2}_{p_2,q_2}(\R^d)$ 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 Schr\"odinger type operators with block-radial potentials. This part essentially relies on the Birman-Schwinger principle.

Author

Dota, Alicja; Skrzypczak, Leszek

Published

2018

Language

EN