On position operator spectral measure for deformed oscillator in the case of indetermine Hamburger moment problem

Borzov, V. V.; Damaskinsky, E. V.; Kulish, P. P.

On position operator spectral measure for deformed oscillator in the case of indetermine Hamburger moment problem

Authors

Borzov, V. V.

Damaskinsky, E. V.

Kulish, P. P.

Description

The spectral measure of the position (momentum) operator $X$ for $q$-deformed oscillator is calculated in the case of the indetermine Hamburger moment problem. The exposition is given for concrete choice of generators for $q$-oscillator algebra, although developed technique apply for every other cases with indetermine moment problem. The Stieltjes transformation $m(z)$ of spectral measure is expressed in terms of the entries of Jacobi matrix $X$ only. The direct connection between values of parameters labeling the spectral measures and related selfadjoint extensions of $X$ is established.
32 pages, LaTeX2e, amssymb,latexsym,amsfonts, no figures