E. W. Lytvynov

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Articles: 10

The projection spectral theorem and Jacobi fields

Eugene Lytvynov

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 21 (2015), no. 2, 188–198

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

A note on equilibrium Glauber and Kawasaki dynamics for permanental point processes

Guanhua Li, Eugene Lytvynov

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 17 (2011), no. 1, 29-46

We construct two types of equilibrium dynamics of an infinite particle system in a locally compact metric space $X$ for which a permanental point process is a symmetrizing, and hence invariant measure. The Glauber dynamics is a birth-and-death process in $X$, while in the Kawasaki dynamics interacting particles randomly hop over $X$. In the case $X=\mathbb R^d$, we consider a diffusion approximation for the Kawasaki dynamics at the level of Dirichlet forms. This leads us to an equilibrium dynamics of interacting Brownian particles for which a permanental point process is a symmetrizing measure.

A note on equilibrium Glauber and Kawasaki dynamics for fermion point processes

Eugene Lytvynov, Nataliya Ohlerich

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 14 (2008), no. 1, 67-80

We construct two types of equilibrium dynamics of infinite particle systems in a locally compact Polish space $X$, for which certain fermion point processes are invariant. The Glauber dynamics is a birth-and-death process in $X$, while in the case of the Kawasaki dynamics interacting particles randomly hop over $X$. We establish conditions on generators of both dynamics under which corresponding conservative Markov processes exist.

An equivalent representation of the Jacobi field of a Lévy process

E. Lytvynov

Methods Funct. Anal. Topology 11 (2005), no. 2, 188-194

On a spectral representation for correlation measures in configuration space analysis

Yuri M. Berezansky, Yuri G. Kondratiev, Tobias Kuna, Eugene Lytvynov

Methods Funct. Anal. Topology 5 (1999), no. 4, 87-100

Analysis and geometry on ${\mathbb R}_{+}$-marked configuration space

Yuri G. Kondratiev, Eugene W. Lytvynov, Georgi F. Us

Methods Funct. Anal. Topology 5 (1999), no. 1, 29-64

Euclidean Gibbs states for quantum continuous systems with Boltzmann statistics via cluster expansion

Yu. G. Kondratiev, A. L. Rebenko, M. Röckner, M. Röckner, G. V. Shchepanʹuk

Methods Funct. Anal. Topology 3 (1997), no. 1, 62-81

Dual Appell systems in non-Gaussian white noise calculus

E. W. Lytvynov, G. F. Us

Methods Funct. Anal. Topology 2 (1996), no. 2, 70-85

A generalization of Gaussian white noise analysis

Yu. M. Berezansky, V. O. Livinsky, E. W. Lytvynov

Methods Funct. Anal. Topology 1 (1995), no. 1, 28-55

Multiple Wiener integrals and non-Gaussian white noises: a Jacobi field approach

E. W. Lytvynov

Methods Funct. Anal. Topology 1 (1995), no. 1, 61-85


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