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

V. V. Borzov·E. V. Damaskinsky·P. P. Kulish
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Abstract

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.

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V. V. Borzov, E. V. Damaskinsky, P. P. Kulish. 1998-03-22. On position operator spectral measure for deformed oscillator in the case of indetermine Hamburger moment problem. https://arxiv.org/abs/math/9803099

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