Zobrazeno 1 - 10
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pro vyhledávání: '"Dereziński, Jan"'
Autor:
Dereziński, Jan, Lee, Jinyeop
Our paper investigates one-dimensional Schr\"odinger operators defined as closed operators on $L^2(\mathbb{R})$ or $L^2(\mathbb{R}_+)$ that are exactly solvable in terms of confluent functions (or, equivalently, Whittaker functions). We allow the pot
Externí odkaz:
http://arxiv.org/abs/2409.14994
Autor:
Dereziński, Jan, Gaß, Christian
We discuss two distinct operator-theoretic settings useful for describing (or defining) propagators associated with a scalar Klein-Gordon field on a Lorentzian manifold $M$. Typically, we assume that $M$ is globally hyperbolic, but we will also consi
Externí odkaz:
http://arxiv.org/abs/2409.03279
Autor:
Dereziński, Jan, Sikorski, Bartłomiej
We review properties of Bessel potentials, that is, inverse Fourier transforms of (regularizations of) $\frac{1}{(m^2+p^2)^{\frac{\mu}{2}}}$ on a pseudoEuclidean space with signature $(q,d-q)$. We are mostly interested in the Lorentzian signature $(1
Externí odkaz:
http://arxiv.org/abs/2406.08327
We review properties of confluent functions and the closely related Laguerre polynomials, and determine their bilinear integrals. As is well-known, these integrals are convergent only for a limited range of parameters. However, when one uses the gene
Externí odkaz:
http://arxiv.org/abs/2404.16539
In dimensions d= 1, 2, 3 the Laplacian can be perturbed by a point potential. In higher dimensions the Laplacian with a point potential cannot be defined as a self-adjoint operator. However, for any dimension there exists a natural family of function
Externí odkaz:
http://arxiv.org/abs/2403.17583
Publikováno v:
J. Phys.: Conf. Ser. 2667 012071 (2023)
First we recall a method of computing scalar products of eigenfunctions of a Sturm-Liouville operator. This method is then applied to Macdonald and Gegenbauer functions, which are eigenfunctions of the Bessel, resp. Gegenbauer operators. The computed
Externí odkaz:
http://arxiv.org/abs/2311.03135
Publikováno v:
Journal of Statistical Physics, 191 (110), 2024
According to the Bogoliubov theory the low energy behaviour of the Bose gas at zero temperature can be described by non-interacting bosonic quasiparticles called phonons. In this work the damping rate of phonons at low momenta, the so-called Beliaev
Externí odkaz:
http://arxiv.org/abs/2310.20070
We compute bilinear integrals involving Macdonald and Gegenbauer functions. These integrals are convergent only for a limited range of parameters. However, when one uses generalized integrals they can be computed essentially without restricting the p
Externí odkaz:
http://arxiv.org/abs/2304.06515