Related papers: Discrete analog of the Jacobi set for vector field…

Given a vector function ${\bf F}=(F_1,\ldots,F_d),$ analytic on a neighborhood of some compact subset $E$ of the complex plane with simply connected complement, we define a sequence of vector rational functions with common denominator in…

In this paper, we introduce the notion of Jacobi polynomials with multiple reference vectors of a code, and give the MacWilliams type identity for it. Moreover, we derive a formula to obtain the Jacobi polynomials using the Aronhold…

We show that for a Jacobi operator with coefficients whose (j+1)'th moments are summable the j'th derivative of the scattering matrix is in the Wiener algebra of functions with summable Fourier coefficients. We use this result to improve…

We describe Jacobi forms of vector-valued weights in terms of classical ones, extending previous results by Ibukiyama and Kyomura to the case of arbitrary cogenus. As in their result, our isomorphisms are given by holomorphic covariant…

We show how Andrews' generating functions for generalized Frobenius partitions can be understood within the theory of Eichler and Zagier as specific coefficients of certain Jacobi forms. This reformulation leads to a recursive process which…

We consider a set of measures on the real line and the corresponding system of multiple orthogonal polynomials (MOPs) of the first and second type. Under some very mild assumptions, which are satisfied by Angelesco systems, we define…

We develop the theory of Hermitian Jacobi forms of lattice index, for both definite and indefinite Hermitian lattices. We also prove a theta decomposition theorem for vector-valued Jacobi forms (both in the orthogonal and Hermitian…

We present here an overview of the history, applications and important properties of a function which we refer to as the Levy integral. For certain values of its characteristic parameter the Levy integral defines the symmetric Levy stable…

The present paper is about Bernstein-type estimates for Jacobi polynomials and their applications to various branches in mathematics. This is an old topic but we want to add a new wrinkle by establishing some intriguing connections with…

We classify all the simple modules for the algebra of relations on a finite set, give their dimension, and find the dimension of the Jacobson radical of the algebra.

A geometric formulation of the linear beam dynamics in accelerator physics is presented. In particular, it is proved that the linear transverse and longitudinal dynamics can be interpret geometrically as an approximation to the Jacobi…

We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…

Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…

Isosurfaces are an important tool for analysis and visualization of univariate scalar fields. Earlier works have demonstrated the presence of interesting isosurfaces at isovalues close to critical values. This motivated the development of…

We define involution algebroids which generalise Lie algebroids to the abstract setting of tangent categories. As a part of this generalisation the Jacobi identity which appears in classical Lie theory is replaced by an identity similar to…

We present certain results on the direct and inverse spectral theory of the Jacobi operator with complex periodic coefficients. For instance, we show that any $N$-th degree polynomial whose leading coefficient is $(-1)^N$ is the Hill…

A representation of the Jacobi algebra $\mathfrak{h}_1\rtimes \mathfrak{su}(1,1)$ by first order differential operators with polynomial coefficients on the manifold $\mathbb{C}\times \mathcal{D}_1$ is presented. The Hilbert space of…

We consider an arbitrary representation of the additive group over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants.

We develop a spectral analysis of a class of block Jacobi operators based on the conjugate operator method of Mourre. We give several applications including scalar Jacobi operators with periodic coefficients, a class of difference operators…

A Hecke action on the space of periods of cusp forms, which is compatible with that on the space of cusp forms, was first computed using continued fraction and an explicit algebraic formula of Hecke operators acting on the space of period…