不定Stieltjes动量问题再审

非确定动量问题的特殊N极值解

Special N-extremal solutions to indeterminate moment problems

本文研究非确定动量问题中的N极值解，证明了当0<α<1时，存在某些解使得(1+x²)^{-α}dμ(x)为确定或非确定，并给出α=1/2时的显式例子。

Self-adjoint difference operators and classical solutions to the Stieltjes--Wigert moment problem

The Stieltjes-Wigert polynomials, which correspond to an indeterminate moment problem on the positive half-line, are eigenfunctions of a second order q-difference operator. We consider the orthogonality measures for which the difference operator is symmetric in the corresponding weighted $L^2$-spaces. These measures are exactly the solutions to the q-Pearson equation.In the case of discrete and absolutely continuous measures the difference operator is essentially self-adjoint, and the corresponding spectral decomposition is given explicitly. In particular, we find an orthogonal set of q-Bessel…

A non-hyponormal operator generating Stieltjes moment sequences

A linear operator $S$ in a complex Hilbert space $\hh$ for which the set $\dzn{S}$ of its $C^\infty$-vectors is dense in $\hh$ and $\{\|S^n f\|^2\}_{n=0}^\infty$ is a Stieltjes moment sequence for every $f \in \dzn{S}$ is said to generate Stieltjes moment sequences. It is shown that there exists a closed non-hyponormal operator $S$ which generates Stieltjes moment sequences. What is more, $\dzn{S}$ is a core of any power $S^n$ of $S$. This is established with the help of a weighted shift on a directed tree with one branching vertex. The main tool in the construction comes from the theory of in…

“矩性质蕴含次正规性”及单回路图上的复合算子单射性问题的解

Solutions to the 'moment property implies subnormality' and injectivity problems for composition operators on one-circuit graphs

本文针对单回路图上的复合算子，完全解决了“矩性质蕴含次正规性”问题，并构造反例否定单射性猜想，确定了最小分支数为2。