Related papers: Two-dimensional algebro-geometric difference opera…
We consider inverse boundary value problems for polyharmonic operators and in particular, the problem of recovering the coefficients of terms up to order one. The main interest of our result is that it further relaxes the regularity…
We give an expression for a generalized numerical radius of Hilbert space operators and then apply it to obtain upper and lower bounds for the generalized numerical radius. We also establish some generalized numerical radius inequalities…
A general method for analytic inversion of geometric integral transforms is proposed
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…
We introduce the notion of Ricci-corrected differentiation in parabolic geometry, which is a modification of covariant differentiation with better transformation properties. This enables us to simplify the explicit formulae for standard…
We introduce a class of multidimensional Schr\"odinger operators with elliptic potential which generalize the classical Lam\'e operator to higher dimensions. One natural example is the Calogero--Moser operator, others are related to the…
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.…
Darboux Transformation, well known in second order differential operator theory, is applied here to the difference equation satisfied by the discrete hypergeometric polynomials(Charlier, Meixner-Krawchuk, Hahn).
We construct a large family of commutative algebras of partial differential operators invariant under rotations. These algebras are isomorphic extensions of the algebras of ordinary differential operators introduced by Grunbaum and Yakimov…
Using simultaneously two operator identities, we consider the inversion of the convolution operators on a rectangular. The structure of the inverse operators and of some corresponding forms, which are important in signal processing, is…
A class of cross-shaped difference operators on a two dimensional lattice is introduced. The main feature of the operators in this class is that their formal eigenvectors consist of multiple orthogonal polynomials. In other words, this…
We consider the standard hypergeometric differential operator $D$ regarded as an operator on the complex plane $C$ and the complex conjugate operator $\overline D$. These operators formally commute and are formally adjoint one to another…
Let $G$ be the identity component of the isometry group for an arbitrary curved two-point homogeneous space $M$. We consider algebras of $G$-invariant differential operators on bundles of unit spheres over $M$. The generators of this…
We present explicit generators of an algebra of commuting difference operators with trigonometric coefficients. The operators are simultaneously diagonalized by recently discovered q-polynomials (viz. Koornwinder's multivariable…
A development of an inverse first-order divided difference operator for functions of several variables is presented. Two generalized derivative-free algorithms builded up from Ostrowski's method for solving systems of nonlinear equations…
We consider factorization problem for differential operators on the commutative algebra of densities (defined either algebraically or in terms of an auxiliary extended manifold) introduced in 2004 by Khudaverdian and Voronov in connection…
In this paper, we study scalar the forth order linear differential operators over an oriented 2-dimensional manifold. We investigate differential invariants of these operators and show their application to the equivalence problem.
In contrast with differential operators on modules over commutative and graded commutative rings, there is no satisfactory notion of a differential operator in noncommutative geometry.
We consider bilinear multipliers that appeared as a distinguished particular case in the classification of two-dimensional bilinear Hilbert transforms by Demeter and Thiele [9]. In this note we investigate their boundedness on Sobolev…
In this paper we study commuting difference operators of rank two. We introduce an equation on potentials $V(n),W(n)$ of the difference operator $L_4=(T+V(n)T^{-1})^2+W(n)$ and some additional data. With the help of this equation we find…