The theory of the classical Jacobi forms on H × C has been studied extensively by Eichler and Zagier[?]. Ziegler[?] developed a more general approach of Jacobi forms of higher degree. In [?] and [?], Gritsenko and Krieg studied Jacobi forms on H × Cn and showed that these kinds of Jacobi forms naturally arise in the Jacobi Fourier expansions of all kinds of automorphic forms in several variable...

Certain “index shifting operators” for local and global representations of the Jacobi group are introduced. They turn out to be the representation theoretic analogues of the Hecke operators Ud and Vd on classical Jacobi forms, which underlie the theory of Jacobi oldand new-forms. Further analogues of these operators on spaces of classical elliptic cusp forms are also investigated. In view of th...

We introduce multiple Wilson polynomials, which give a new example of multiple orthogonal polynomials (Hermite-Padé polynomials) of type II. These polynomials can be written as a Jacobi-Piñeiro transform, which is a generalization of the Jacobi transform for Wilson polynomials, found by T.H. Koornwinder. Here we need to introduce Jacobi and JacobiPiñeiro polynomials with complex parameters. Som...

This paper gives three theorems regarding functions integrable on [−1, 1] with respect to Jacobi weights, and having nonnegative coefficients in their (Fourier–)Jacobi expansions. We show that the L-integrability (with respect to the Jacobi weight) on an interval near 1 implies the L-integrability on the whole interval if p is an even integer. The Jacobi expansion of a function locally in L∞ ne...

In this paper we give evidence to show that in onesided Jacobi SVD computation the sorting of column norms in each sweep is very important. Two parallel Jacobi orderings are described. These orderings can generate n(n 1)=2 di erent index pairs and sort column norms at the same time. The one-sided Jacobi SVD algorithm using these parallel orderings converges in about the same number of sweeps as...

In this paper we investigate Donder-Weyl (DW) Hamilton-Jacobi equations and establish the connection between DW Hamilton-Jacobi equations and multi-symplectic Hamiltonian systems. Based on the study of DW Hamilton-Jacobi equations, we present the generating functions for multi-symplectic partitioned Runge-Kutta (PRK) methods.

We show that Nambu-Poisson and Nambu-Jacobi brackets can be defined inductively: an n-bracket, n > 2, is Nambu-Poisson (resp. Nambu-Jacobi) if and only if fixing an argument we get an (n − 1)-Nambu-Poisson (resp. Nambu-Jacobi) bracket. As a by-product we get relatively simple proofs of Darboux-type theorems for these structures.

We show that Nambu-Poisson and Nambu-Jacobi brackets can be defined inductively: an n-bracket, n > 2, is Nambu-Poisson (resp. Nambu-Jacobi) if and only if fixing an argument we get an (n − 1)-Nambu-Poisson (resp. Nambu-Jacobi) bracket. As a by-product we get relatively simple proofs of Darboux-type theorems for these structures.