Related papers: The Sobolev moment problem and Jordan dilations

A theory of Sobolev inequalities in arbitrary open sets of Euclidean space is established. Boundary regularity of domains is replaced with information on boundary traces of trial functions and of their derivatives up to some explicit…

We consider extremal polynomials with respect to a Sobolev-type $p$-norm, with $1<p<\infty$ and measures supported on compact subsets of the real line. For a wide class of such extremal polynomials with respect to mutually singular measures…

In this work, a mixed problem for a time-fractional equation with a delayed argument and pseudodifferential operators related to Laplace operators with non-local boundary conditions in Sobolev classes is studied. The solutions to the…

The authors present a unified method for calculating the zeros of the classical orthogonal polynomials based upon the electrostatic interpretation and its connection to the energy minimization problem. Examples are given with error…

This is a survey of known results on estimating the principal Lyapunov exponent of a time-dependent linear differential equation possessing some monotonicity properties. Equations considered are mainly strongly cooperative systems of…

We introduce a restricted four body problem in a 2+2 configuration extending the classical Sitnikov problem to the Double Sitnikov problem. The secondary bodies are moving on the same perpendicular line to the planewhere the primaries…

In contrast to mono-constrained flows with N degrees of freedom, binary constrained flows of soliton equations, admitting 2x2 Lax matrices, have 2N degrees of freedom. By means of the existing method, Lax matrices only yield the first N…

We consider linear, time-dependent and skew-adjoint perturbations of periodic transport equations on the one-dimensional torus. We describe the long-time behavior of solutions for all non-degenerate perturbations in resonant regime, proving…

We look for spectral type differential equations for the generalized Jacobi polynomials and for the Sobolev-Laguerre polynomials. We use a method involving computeralgebra packages like Maple and Mathematica and we will give some…

We consider Poisson's equation with a finite number of weighted Dirac masses as a source term, together with its discretization by means of conforming finite elements. For the error in fractional Sobolev spaces, we propose residual-type a…

Classically, a single weight on an interval of the real line leads to moments, orthogonal polynomials and tridiagonal matrices. Appropriately deforming this weight with times t=(t_1,t_2,...), leads to the standard Toda lattice and…

Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial…

This is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators. Among the advantages of this approach is that the Nevanlinna functions appear as elements of a transfer matrix…

In this note we give a survey about polynomials whose moments are multiples of super Catalan numbers and explore two different kinds of q-analogues.

In this survey we discuss some of the classical and modern methods in studying the (Riemann-)Schottky problem, the problem of characterizing Jacobians of curves among principally polarized abelian varieties. We present many of the recent…

We construct new examples of exceptional Hahn and Jacobi polynomials. Exceptional polynomials are orthogonal polynomials with respect to a measure which are also eigenfunctions of a second order difference or differential operator. The most…

We solve the difference equation with linear coefficients by the Momentenansatz to obtain explicit formulas for orthogonal polynomials.

The existence of extremal functions for the Sobolev trace inequalities is studied using the concentration compactness theorem. The conjectured extremal, the function of conformal factor, is considered and is proved to be an actual extremal…

We consider polynomials that are orthogonal over an analytic Jordan curve L with respect to a positive analytic weight, and show that each such polynomial of sufficiently large degree can be expanded in a series of certain integral…

We study mathematically a system of partial differential equations arising in the modelling of an aging fluid, a particular class of non Newtonian fluids. We prove well-posedness of the equations in appropriate functional spaces and…