A new method of evaluating overlap integrals involving orthogonal polynomials is proposed. The technique relies on purely algebraic manipulation of the associated recurrence coefficients. For a large class of polynomials and for sufficiently large orders, these coefficients can be written explicitly as Taylor series in terms of powers of = 1/n, where n is the polynomial order. Such decompositio...

We present novel Markov-type and Nikolskii-type inequalities for multivariate polynomials associated with arbitrary downward closed multi-index sets in any dimension. Moreover, we show how the constant of these inequalities changes, when the polynomial is expanded in series of tensorized Legendre or Chebyshev or Gegenbauer or Jacobi orthogonal polynomials indexed by a downward closed multi-inde...

We study codes over a finite field F4. We relate self-dual codes over F4 to real 5-modular lattices and to self-dual codes over F2 via a Gray map. We construct Jacobi forms over Q( √ 5) from the complete weight enumerators of self-dual codes over F4. Furthermore, we relate Hilbert–Siegel forms to the joint weight enumerators of self-dual codes over F4. © 2004 Elsevier Ltd. All rights reserved.

Using some well known concepts on orthogonal polynomials, some recent results on the location of eigenvalues of tridiagonal matrices of very large order are extended. A significant number of important papers are unified. c © 2006 Elsevier Ltd. All rights reserved.

Let e ⊂ R be a finite union of l + 1 disjoint closed intervals and denote by ωj the harmonic measure of the j leftmost bands. The frequency module for e is the set of all integral combinations of ω1, . . . , ωl. Let {ãn, b̃n}n=1 be a point in the isospectral torus for e and p̃n its orthogonal polynomials. Let {an, bn}n=1 be a half-line Jacobi matrix with an = ãn+δan, bn = b̃n+δbn. Suppose

Starting from Jacobi-Trudi’s type determinental expressions for the Schur functions corresponding to types B,C and D, we define a natural q-analogue of the multiplicity [V (λ) : M(μ)] when M(μ) is a tensor product of row or column shaped modules defined by μ. We prove that these q-multiplicities are equal to certain Kostka-Foulkes polynomials related to the root systems C or D. Finally we deriv...

Let e ⊂ R be a finite union of + 1 disjoint closed intervals, and denote by ωj the harmonic measure of the j left-most bands. The frequency module for e is the set of all integral combinations of ω1, . . . ,ω . Let {ãn, b̃n}∞n=−∞ be a point in the isospectral torus for e and p̃n its orthogonal polynomials. Let {an, bn}∞n=1 be a half-line Jacobi matrix with an = ãn + δan, bn = b̃n + δbn. Suppose ∞ ...

We exhibit 3 families of complete curvature homogeneous pseudo-Riemannian manifolds which are modeled on irreducible symmetric spaces and which are not locally homogeneous. All of the manifolds have nilpotent Jacobi operators; some of the manifolds are, in addition, Jordan Osserman and Jordan Ivanov-Petrova.

Using spectral theory of unitary operators and the theory of orthogonal polynomials on the unit circle, we propose a simple matrix model for the following circular analogue of the Jacobi ensemble:

We describe the asymptotic behavior of the multivariate BC–type Jacobi polynomials as the number of variables and the Young diagram indexing the polynomial go to infinity. In particular, our results describe the approximation of the spherical functions of the infinite-dimensional symmetric spaces of type B, C, D or BC by the spherical functions of the corresponding finite–dimensional symmetric ...