English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We discuss a model of a $q$-harmonic oscillator based on Rogers-Szeg\H{o}functions. We combine these functions with a class of $q$-analogs of complexHermite polynomials to construct a new set of coherent states depending on anonnegative integer parameter $m$. Our construction leads to a new$q$-deformation of the $m$-true-polyanalytic Bargmann transform whose rangedefines a generalization of the Arik-Coon space. We also give an explicitformula for the reproducing kernel of this space. The obtained results may beexploited to define a $q$-deformation of the Ginibre-$m$-type process on thecomplex plane.

A set of $q$-coherent states for the Rogers-Szeg\H{o} oscillator