E. Lytvynov

activity

20022023

most citedFunctional spaces and operators connected with some Lévy noises

2 citations · 4 across the 9 of their papers we have counts for

collaborators

10 papers

math-ph2023

Quasi-free states on a class of algebras of multicomponent commutation relations

Eugene Lytvynov, Nedal Othman

Multicomponent commutations relations (MCR) describe plektons, i.e., multicomponent quantum systems with a generalized statistics. In such systems, exchange of quasiparticles is go…

math.PR2016

Meixner class of orthogonal polynomials of a non-commutative monotone Levy noise

Eugene Lytvynov, Irina Rodionova

Let $(X_{t})_{t \geq 0}$ denote a non-commutative monotone Lévy process. Let $ω = (ω (t))_{t \geq 0}$ denote the corresponding monotone Lévy noise.. A continuous polynomial of $ω$ is an eleme…

math.PR2015

The projection spectral theorem and Jacobi fields

Eugene Lytvynov

We review several applications of Berezansky's projection spectral theorem to Jacobi fields in a symmetric Fock space, which lead to Lévy white noise measures.

math.PR2013

An extended anyon Fock space and noncommutative Meixner-type orthogonal polynomials in infinite dimensions

Marek Bozejko, Eugene Lytvynov, Irina Rodionova

Let $ν$ be a finite measure on $R$ whose Laplace transform is analytic in a neighborhood of zero. An anyon Lévy white noise on $(R^{d}, d x)$ is a certain family of non…

math.PR2008

Lowering and raising operators for the free Meixner class of orthogonal polynomials

Eugene Lytvynov, Irina Rodionova

We compare some properties of the lowering and raising operators for the classical and free classes of Meixner polynomials on the real line.

math.PR2006★ 2 cited

Functional spaces and operators connected with some Lévy noises

E. Lytvynov

We review some recent developments in white noise analysis and quantum probability. We pay a special attention to spaces of test and generalized functionals of some Lévy white nois…