块径向势函数和Schr dinger型算子的一些性质
Some properties of block-radial functions and Schrödinger type operators with block-radial potentials
摘要：
设$ R_γB^{s}_{p,q}(\Rd)$是Besov空间$B^{s}_{p,q}(\Rd)$的由块径向函数组成的子空间。我们证明了紧嵌入$\id: \: R_γB^{s_1}_{p_1,q_1}(\R^d) \rightarrow R_γB^{s_2}_{p_2,q_2}(\R^d)$的熵数的渐近行为依赖于最低维的块的数目，参数$p_1$和$p_2$，但独立于光滑参数$s_1$，$s_2$。我们应用的渐近行为估计的薛定谔型运营商与块径向潜力的负谱的权力。这一部分基本上依赖于Birman-Schwinger原则。
英文摘要：
Let $ R_γB^{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 $\id: \: R_γB^{s_1}_{p_1,q_1}(\R^d) \rightarrow R_γB^{s_2}_{p_2,q_2}(\R^d)$ 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 Schrödinger type operators with block-radial potentials. This part essentially relies on the Birman-Schwinger principle.
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