Related papers: Multiple Geronimus transformations
We introduce G{\aa}rding polynomials, a class of real multivariate polynomials characterized by positivity regions that are invariant under translation by positive vectors and closed under strictly positive affine transformations. We prove…
The discrete cosine transform is a valuable tool in analysis of data on undirected rectangular grids, like images. In this paper it is shown how one can define an analogue of the discrete cosine transform on triangles. This is done by…
We study a family of Laguerre--Sobolev orthogonal polynomials associated with a Sobolev inner product arising from second--order boundary value problems on the semi--infinite interval $(0,+\infty)$. These polynomials generate an orthogonal…
We consider multiple orthogonal polynomials corresponding to two Macdonald functions (modified Bessel functions of the second kind), with emphasis on the polynomials on the diagonal of the Hermite-Pad\'e table. We give some properties of…
Heterotic toriodal Z2xZ2 orbifolds may possess discrete torsion between the two defining orbifold twists in the form of additional cocycle factors in their one-loop partition functions. Using Gauged Linear Sigma Models (GLSMs) the…
Penrose transform tells us that there is an isomorphism of the kernel of an invariant differential operator studied in the paper [TS] and sheaf cohomology of some vector bundle on twistor space. The point of this paper is to write down this…
In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product. These properties are then utilized…
We prove two "master" convolution theorems for multivariate determinantal polynomials. The methods used include basic properties of what we call a "minor-orthogonal" ensemble as well as properties of the mixed discriminant of matrices. We…
We demonstrate general classifications of Riemann surface topology generated by multiple arbitrary-order exceptional points of quasi-stationary states. Our studies reveal all possible product permutations of holonomy matrices that describe…
In this paper we investigate multiple polylogarithms with non-positive multi-indices (nonpositive MPLs) from a combinatorial and algebraic viewpoint. By introducing a correspondence between non-positive multiple polylogarithms and Magnus…
In math/0702157, arXiv:0712.4185, we investigated monic multivariate non-commutative orthogonal polynomials, their recursions, states of orthogonality, and corresponding continued fraction expansions. In this note, we collect a number of…
In this contribution we consider sequences of monic polynomials orthogonal with respect to Sobolev-type inner product \[ \left\langle f,g\right\rangle= \langle {\bf u}^{\tt M},fg\rangle+\lambda \mathscr T^j f (\alpha)\mathscr…
In this review we summarise recent results for the complex eigenvalues and singular values of finite products of finite size random matrices, their correlation functions and asymptotic limits. The matrices in the product are taken from…
The goal of this work is to characterize all second order difference operators of several variables that have discrete orthogonal polynomials as eigenfunctions. Under some mild assumptions, we give a complete solution of the problem.
We consider matrix orthogonal polynomials related to Jacobi type matrices of weights that can be defined in terms of a given matrix Pearson equation. Stating a Riemann-Hilbert problem we can derive first and second order differential…
We are concerned with polynomial involutions in characteristic two. In this note, we look for involutions among triangular automorphisms of the four-dimensional polynomial ring in characteristic two and obtain three types of such…
In this note, we shall provide several properties of hypergeometric Bernoulli numbers and polynomials, including sums of products identity, differential equations and recurrence formulas.
We analyze nonlinear collective effects near surfaces of semi-infinite periodic systems with multi-gap transmission spectra and introduce a novel concept of multi-gap surface solitons as mutually trapped surface states with the components…
Given n quaternions we investigate the extent of non-commutativity of their multiple products, commutators and exponential products.
We consider diagonal matrix elements of local operators between multi-soliton states in finite volume in the sine-Gordon model, and formulate a conjecture regarding their finite size dependence which is valid up to corrections exponential…