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Maciej Karczmarczyk

Publications and source records attributed to Maciej Karczmarczyk.

3 recordsLinked to original sources
arXiv2017

Quantization of Gaussians

Our paper is devoted to the oscillator semigroup, which can be defined as the set of operators whose kernels are centered Gaussian. Equivalently, they can be defined as the the Weyl quantization of centered Gaussians. We use the Weyl symbol as the main parametrization of this semigroup. We derive formulas for the tracial and operator norm of the Weyl quantization of Gaussians. We identify the subset of Gaussians, which we call quantum degenerate, where these norms have a singularity.

math-ph↗
arXiv2017

Equations of hypergeometric type in the degenerate case

We consider the three most important equations of hypergeometric type, ${}_2F_1$, ${}_1F_1$ and ${}_1F_0$, in the so-called degenerate case. In this case one of the parameters, usually denoted $c$, is an integer and the standard basis of solutions consists of a hypergeometric-type function and a function with a logarithmic singularity. This article is devoted to a thorough analysis of the latter solution to all three equations.

math-ph↗