Related papers: Biorthonormal Systems in Freud-type Weighted Space…
This work is a thorough investigation of skew-orthogonal polynomials with respect to a quartic Freud weight. We provide an explicit method to evaluate skew-orthogonal polynomials of any degree as linear combinations of orthogonal…
The connection between continued fractions and orthogonality which is familiar for $J$-fractions and $T$-fractions is extended to what we call $R$-fractions of type I and II. These continued fractions are associated with recurrence…
A new isomorphism invariant of matroids is introduced, in the form of a quasisymmetric function. This invariant (1) defines a Hopf morphism from the Hopf algebra of matroids to the quasisymmetric functions, which is surjective if one uses…
This paper analyzes the structure of the set of nodal solutions of a class of one-dimensional superlinear indefinite boundary values problems with an indefinite weight functions in front of the spectral parameter. Quite astonishingly, the…
In this paper the controllabillity and admissibility of perturbed semigroup systems are studied, using tools from the theory of interpolation and Carleson measures. In addition, there are new results on the perturbation of Carleson measures…
We discuss the relationship between the recurrence coefficients of orthogonal polynomials with respect to a generalized Freud weight \[w(x;t)=|x|^{2\lambda+1}\exp\left(-x^4+tx^2\right),\qquad x\in\mathbb{R},\] with parameters $\lambda>-1$…
We describe recent achievements in the theory of weight systems, which are functions on chord diagrams satisfying so-called $4$-term relations. Our main attention is devoted to constructions of weight systems. The two main sources of these…
To compute solutions of sparse polynomial systems efficiently we have to exploit the structure of their Newton polytopes. While the application of polyhedral methods naturally excludes solutions with zero components, an irreducible…
This paper introduces an interpolation framework for the weighted-H2 model reduction problem. We obtain a new representation of the weighted-H2 norm of SISO systems that provides new interpolatory first order necessary conditions for an…
In this paper we consider two different nonlinear $\sigma$-models minimally coupled to Eddington-inspired Born-Infeld gravity. We show that the resultant geometries represent minimal modifications with respect to those found in GR, though…
We study bivariate orthogonal polynomials associated with Freud weight functions depending on real parameters. We analyze relations between the matrix coefficients of the three term relations for the orthonormal polynomials as well as the…
We calculate the small quantum orbifold cohomology of arbitrary weighted projective spaces. We generalize Givental's heuristic argument, which relates small quantum cohomology to S^1-equivariant Floer cohomology of loop space, to weighted…
We characterize sampling and interpolating sets with derivatives in weighted Fock spaces on the complex plane in terms of their weighted Beurling densities.
We use techniques from Gromov-Witten theory to construct new invariants of matroids taking value in the Chow groups of spaces of rational curves in the permutohedral toric variety. When the matroid is realizable by a complex hyperplane…
Multiple orthogonality is considered in the realm of a Gauss--Borel factorization problem for a semi-infinite moment matrix. Perfect combinations of weights and a finite Borel measure are constructed in terms of M-Nikishin systems. These…
The notion of disjoint weighing matrices is introduced as a generalization of orthogonal designs. A recursive construction along with a computer search lead to some infinite classes of disjoint weighing matrices, which in turn are shown to…
The singularity structure of cosmological models whose matter content consists of a scalar field with arbitrary non-negative potential is discussed. The special case of spatially flat FRW space-time is analysed in detail using a dynamical…
Superintegrable systems are classical and quantum Hamiltonian systems which enjoy much symmetry and structure that permit their solubility via analytic and even, algebraic means. They include such well-known and important models as the…
The two-matrix model can be solved by introducing bi-orthogonal polynomials. In the case the potentials in the measure are polynomials, finite sequences of bi-orthogonal polynomials (called "windows") satisfy polynomial ODEs as well as…
We propose iterative inversion algorithms for weighted Radon transforms $R_W$ along hyperplanes in $R^3$. More precisely, expandingthe weight $W = W (x, \theta), x \in R^3 , \theta \in S^2$ , into the series of spherical harmonics in…