Related papers: Transition function for the Toda chain model
In this paper, we consider the problem of quantifying controllability and observability of a nonlinear discrete time dynamical system. We introduce the Koopman operator as a canonical representation of the system and apply a lifting…
We investigate the form of equilibrium spatio-temporal correlation functions of conserved quantities, and of energy transport in the Toda lattice and in other integrable models. From numerical simulations we find that the correlations…
We propose a fast, optimization-free method for learning the transition operators of high-dimensional Markov processes. The central idea is to perform a Galerkin projection of the transition operator to a suitable set of low-order bases…
We develop direct and inverse scattering theory for Jacobi operators with steplike quasi-periodic finite-gap background in the same isospectral class. We derive the corresponding Gel'fand-Levitan-Marchenko equation and find minimal…
Using the n-particle periodic Toda lattice and the relativistic generalization due to Ruijsenaars of the elliptic Calogero-Moser system as examples, we revise the basic properties of the Baecklund transformations (BT's) from the Hamiltonian…
This paper establishes a Transition Path Theory (TPT) for L\'{e}vy-type processes, addressing a critical gap in the study of the transition mechanism between meta-stabile states in non-Gaussian stochastic systems. A key contribution is the…
Squared eigenfunctions are quadratic combinations of Jost functions and adjoint Jost functions which satisfy the linearized equation of an integrable equation. In this article, squared eigenfunctions are derived for the Sasa-Satsuma…
The paper is concerned with the doubling estimates and vanishing order of the Steklov eigenfunction on the boundary of a smooth boundary domain $\mathbb R^n$. The eigenfunction is given by a Dirichlet-to-Neumann map. We improve the doubling…
The average of the ratio of powers of the spectral determinants of the Dirac operator in the $\epsilon$-regime of QCD is shown to satisfy a Toda lattice equation. The quenched limit of this Toda lattice equation is obtained using the…
We construct representation of the Separated Variables (SoV) for the quantum SL(2,R) Heisenberg closed spin chain and obtain the integral representation for the eigenfunctions of the model. We calculate explicitly the Sklyanin measure…
This is an extended version of originally published survey in the book: "Advances in Modern Analysis and Mathematical Modeling". Editors: Yu.F.Korobeinik, A.G.Kusraev. Vladikavkaz: Vladikavkaz Scientific Center, of the Russian Academy of…
The Chernoff approximation method is a powerful and flexible tool of functional analysis, which allows in many cases to express exp(tL) in terms of variable coefficients of a linear differential operator L. In this paper, we prove a theorem…
In this work, we examine spectral properties of Markov transition operators corresponding to Gaussian perturbations of discrete time dynamical systems on the circle. We develop a method for calculating asymptotic expressions for eigenvalues…
In this paper, we study infinite dimensional stochastic systems having both unbounded control and observation operators. First of all, using a semigroup approach, we give another take of the well-posedness of such systems treated in [SIAM…
This work serves as a bridge between two approaches to analysis of dynamical systems: the local, geometric analysis and the global, operator theoretic, Koopman analysis. We explicitly construct vector fields where the instantaneous Lyapunov…
Using a stochastic representation provided by Wiener-regularized path integrals for the semigroups generated by certain Berezin-Toeplitz operators, a transformation formula for their resolvents is derived. The key property used in the…
Recently Strachan introduced a Moyal algebraic deformation of selfdual gravity, replacing a Poisson bracket of the Plebanski equation by a Moyal bracket. The dressing operator method in soliton theory can be extended to this Moyal algebraic…
In this article $\lambda$-method of Mitrinovic-Vasic \cite{MitrinovicVasic70} is applied to improve the upper bound for the arcsin function of L. Zhu \cite{Zhu05} for inequalities of Shafer-Fink's type.
In this article, we describe an efficient method for computing Teitelbaum's $p$-adic $\mathcal{L}$-invariant. These invariants are realized as the eigenvalues of the $\mathcal{L}$-operator acting on a space of harmonic cocycles on the…
In this paper, we present an explicit formula that connects the Kontsevich-Witten tau-function and the Hodge tau-function by differential operators belonging to the $\hat{GL(\infty)}$ group. Indeed, we show that the two tau-functions can be…