23 citations · 49 across the 12 of their papers we have counts for
10 papers
Umbral calculus over a vector space
Abdullah Alharthi, Eugene Lytvynov
Let be a vector space over or . We develop a basis-free umbral calculus over . We define the vector space of polynomials over , and polyn…
Generalized Segal-Bargmann transform for Poisson distribution revisited
Chadaphorn Kodsueb, Eugene Lytvynov
For and , we consider the following probability distribution on : $π_{α,σ} = \exp \big(- \fracσ{α^2}\big) \sum_{n=0}^{\infty} \frac{1}{n!} \big(\fracσ{α^2…
Segal-Bargmann transforms and generalized Weyl algebras associated with the Meixner class of orthogonal polynomials
Chadaphorn Kodsueb, Eugene Lytvynov
Meixner (1934) proved that there exist exactly five classes of orthogonal Sheffer sequences: Hermite polynomials which are orthogonal with respect to Gaussian distribution, Charlie…
Finite difference calculus in the continuum
Dmitri Finkelshtein, Yuri Kondratiev, Eugene Lytvynov +1
The paper describes known and new results about finite difference calculus on configuration spaces. We describe finite difference geometry on configuration spaces, connect finite d…
Laplace operators on differential forms over configuration spaces
S. Albeverio, A. Daletskii, E. Lytvynov
Spaces of differential forms over configuration spaces with Poisson measures are constructed. The corresponding Laplacians (of Bochner and de Rham type) on forms and associated sem…
De Rham cohomology of configuration spaces with Poisson measure
S. Albeverio, A. Daletskii, E. Lytvynov
The space of all locally finite configurations in a Riemannian manifold of infinite volume is considered. The deRham complex of square-integrable differential forms over…