Related papers: The characterization problem for one class high or…

The solution of the continuous time filtering problem can be represented as a ratio of two expectations of certain functionals of the signal process that are parametrized by the observation path. We introduce a class of discretization…

This work develops a framework to discover relations between the components of the solution to a given initial-value problem for a first-order system of ordinary differential equations. This is done by using sparse identification techniques…

In this paper, we introduce some analytical techniques to solve some classes of second order differential equations. Such classes of differential equations arise in describing some mathematical problems in Physics and Engineering.

For a large class of integral operators or second order differential operators, their isospectral (or cospectral) operators are constructed explicitly in terms of $h$-transform (duality). This provides us a simple way to extend the known…

Optimal approximation and optimal interpolation problems on the classes of periodic functions that are determined by restrictions on several higher derivatives of the functions are solved.

Symbolic recovery of differential equations is the ambitious attempt at automating the derivation of governing equations with the use of machine learning techniques. In contrast to classical methods which assume the structure of the…

In this paper we continue the study (initiated in arXiv:2003.13584) of the semiclassical behavior of the scattering data of a non-self-adjoint Dirac operator with a real, positive, fairly smooth but not necessarily analytic potential…

In this paper, we briefly explain the spectral expansion problem for differential operators defined on the entire real line, generated by a differential expression with periodic, complex-valued coefficients.

For a Dirac operator with non-local potential on a finite segment, a method of reconstruction of non-local potential from the spectral data is developed. Description of spectral data for such class of operators is given.

We provide a probabilistic characterization of criticality, subcriticality, and supercriticality for subordinated Schr\"{o}dinger operators. We also investigate the relationship between the subcriticality of these operators and the uniform…

The first part of the paper is a survey of some of the results previously obtained by the authors concerning the $L^p$-dissipativity of scalar and matrix partial differential operators. In the second part we give new necessary and,…

This talk is devoted mainly to the concept of higher-order polarization on a group, which is introduced in the framework of a Group Approach to Quantization, as a powerful tool to guarantee the irreducibility of quantizations and/or…

In the work, the property of the second-order subdifferential is studied and second-order optimality conditions are obtained for the minimization problem. We also obtained necessary and sufficient conditions for an extremum for the extremal…

In this paper, we study one of the fundamental notions in dynamical systems, the shadowing of invertible (bounded and linear) operators on a Hilbert space. Although the problem of finding a spectral characterization for shadowing has been…

Aspects of the theory of characteristic modes, based on their variational formulation, are presented and an explicit form of a related functional, involving only currents in a spatial domain, is derived. The new formulation leads to deeper…

In this paper, we consider a regularization strategy for the factorization method when there is noise added to the data operator. The factorization method is a qualitative method used in shape reconstruction problems. These methods are…

The identification of dynamics from time series data is a problem of general interest. It is well established that dynamics on the level of invariant sets, the primary objects of interest in the classical theory of dynamical systems, is not…

This paper studies the problem of state estimation for linear time-invariant descriptor systems in their most general form. The estimator is a system of ordinary differential equations (ODEs). We introduce the notion of partial causal…

This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and…

Scattering problem for a self-adjoint integro-differential operator, which is the sum of the operator of second derivative and of a finite-dimensional self-adjoint operator, is studied. Jost solutions are found and it is shown that the…