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

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

Quantum Algebra 2007-05-23 v1

Authors: V. V. Borzov , E. V. Damaskinsky , P. P. Kulish

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.

Keywords

q-deformed oscillator position operator spectral measure indeterminate hamburger moment problem jacobi matrix selfadjoint extensions

Cite

@article{arxiv.math/9803099,
  title  = {On position operator spectral measure for deformed oscillator in the case of indetermine Hamburger moment problem},
  author = {V. V. Borzov and E. V. Damaskinsky and P. P. Kulish},
  journal= {arXiv preprint arXiv:math/9803099},
  year   = {2007}
}

Comments

32 pages, LaTeX2e, amssymb,latexsym,amsfonts, no figures

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

Abstract

Keywords

Cite

Comments

Related papers