相关论文: Buschman-Erdelyi transmutations, classification an…

The notion of singular reduction operators, i.e., of singular operators of nonclassical (conditional) symmetry, of partial differential equations in two independent variables is introduced. All possible reductions of these equations to…

I recent years, studying degenerate versions of some special polynomials, which was initiated by Carlitz in an investigation of the degenerate Bernoulli and Euler polynomials, regained lively interest of mant mathematicains. In this paper,…

Monotone operators are of basic importance in optimization as they generalize simultaneously subdifferential operators of convex functions and positive semidefinite (not necessarily symmetric) matrices. In 1970, Asplund studied the additive…

In this note, under a certain assumption on an affine space of operators, which admit embedded eigenvalues, it is shown that the singular part of the spectral shift function of any pair of operators from this space is an integer-valued…

The present paper deals with modifications of Bernstein, Kantorovich, Durrmeyer and genuine Bernstein-Durrmeyer operators. Some previous results are improved in this study. Direct estimates for these operators by means of the first and…

This is a survey, which is a continuation of the previous survey of the author about applications of Carleman estimates to Inverse Problems, J. Inverse and Ill-Posed Problems, 21, 477-560, 2013. It is shown here that Tikhonov functionals…

The techniques developed by Popescu, Muhly-Solel and Good for the study of algebras generated by weighted shifts are applied to generalize results of Sarkar and of Bhattacharjee-Eschmeier-Keshari-Sarkar concerning dilations and invariant…

Spectral properties od Delsarte transmutation operators are studied, their differential geometrical and topological structure in multidimension is analyzed, the relationships with De Rham-Hodge-Skrypnik theory of generalized differential…

We will present versions of the Rellich-Kondrachov theorem for pseudo-differential operators acting on localizable Hardy spaces. One of the techniques includes boundedness properties for pseudodifferential operators with symbols in the…

The goal of this paper is to introduce the notion of polyconvolution for Fourier-cosine, Laplace integral operators, and its applications. The structure of this polyconvolution operator and associated integral transforms are investigated in…

B\"acklund transformations (BTs) are traditionally regarded as a tool for integrating nonlinear partial differential equations (PDEs). Their use has been recently extended, however, to problems such as the construction of recursion…

I review the concept of a {\em disorder operator}, introduced originally by Kadanoff in the context of the two-dimensional Ising model. Disorder operators acquire an expectation value in the disordered phase of the classical spin system.…

Boshernitzan found a decay condition on the measure of cylinder sets that implies unique ergodicity for minimal subshifts. Interest in the properties of subshifts satisfying this condition has grown recently, due to a connection with the…

In his seminal 1934 paper on Brownian motion and the theory of gases Kolmogorov introduced a second order evolution equation which displays some challenging features. In the opening of his 1967 hypoellipticity paper H\"ormander discussed a…

We introduce a new family of invariant differential operators associated with $\lambda$-cosine and Funk-Radon transforms on Stiefel and Grassmann manifolds. These operators reduce the order of the $\lambda$-cosine transforms and yield new…

We study some complete orthonormal systems on the real-line. These systems are determined by Bargmann-type transforms, which are Fourier integral operators with complex-valued quadratic phase functions. Each system consists of…

We give an in-depth study of the Tchebyshev transforms of the first and second kind of a poset, recently discovered by Hetyei. The Tchebyshev transform (of the first kind) preserves desirable combinatorial properties, including Eulerianess…

In the first part of this series of papers we developed the invariant differentiation with respect to a Cartan connection, we described this procedure in the terms of the underlying principal connections, and we discussed applications of…

We consider an analog of the problem Veblen formulated in 1928 at the IMC: classify invariant differential operators between "natural objects" (spaces of either tensor fields, or jets, in modern terms) over a real manifold of any dimension.…

Neural operator learning models have emerged as very effective surrogates in data-driven methods for partial differential equations (PDEs) across different applications from computational science and engineering. Such operator learning…