We show asymptotic expansions of the eigenfunctions certain perturbations Jacobi operator in a bounded interval, deducing equiconvergence results between with respect to associated orthonormal basis and cosine basis. Several for pointwise convergence then follow.

The little q-Jacobi function transform depends on three parameters. An explicit expression as a sum of two very-well-poised 8W7-series is derived for the dual transmutation kernel relating little q-Jacobi function transforms for different parameter sets. A product formula for the dual transmutation kernel is obtained. For the inverse transform the transmutation kernel is given as a 3φ2-series, ...

Jacobi-like forms of one variable are formal power series with holomorphic coefficients satisfying a certain transformation formula with respect to the action of a discrete subgroup Γ of SL(2,R), and they are related to modular forms for Γ, which of course play a major role in number theory. Indeed, by using this transformation formula, it can be shown that that there is a one-to-one correspond...

Jacobi polynomials were introduced by Ozeki in analogy with Jacobi forms of lattices They are useful for coset weight enumeration and weight enumeration of children We determine them in most interesting cases in length at most and in some cases in length We use them to construct group divisible designs packing designs covering designs and t r designs in the sense of Calderbank Delsarte A major ...

Classically, there are many interesting connections between differential operators and the theory of elliptic modular forms and many interesting results have been explored. In particular, it has been known for some time how to obtain an elliptic modular form from the derivatives ofN elliptic modular forms, which has already been studied in detail by R. Rankin in [9] and [10]. When N = 2, as a s...

In this paper, a Jacobi-collocation spectral method is developed for Volterra integral equations of second kind with a weakly singular kernel. We use some function transformation and variable transformations to change the equation into a new Volterra integral equation defined on the standard interval [−1, 1], so that the solution of the new equation possesses better regularity and the Jacobi or...

The periodic Jacobi inverse eigenvalue problem concerns the reconstruction of a matrix from prescribed spectral data. In Minkowski spaces, with given signature operator H=diag(1,1,…,1,?1), corresponding is pseudo-Jacobi matrix. for such matrices consists in matrices, same order and H. this paper we solve by applying Sylvester’s identity Householder transformation. solution number algorithm are ...

We present a new technique to obtain polynomial decay estimates for the matrix coefficients of unitary operators. Our approach, based on commutator methods, applies nets operators, representations topological groups, and operators given by evolution group self-adjoint operator or powers operator. results are illustrated with wide range examples in quantum mechanics dynamical systems, as instanc...