Showing papers by "William Desmond Evans published in 1994"
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TL;DR: In this article, the adjoint of the Askey-Wilson divided difference operator with respect to the inner procuct on L^2(-1,1,(1-x^2)^-1/2 dx) defined as a Cauchy principle value was found.
Abstract: We find the adjoint of the Askey-Wilson divided difference operator with respect to the inner procuct on L^2(-1,1,(1-x^2)^-1/2 dx) defined as a Cauchy principle value and show that the Askey-Wilson polynomials are solutions of a q-Sturm-Liouville problem. From these facts we deduce various properties of the polynomials in a simple and straightforward way. We also provide an operator theoretic description of the Askey-Wilson operator.
23Â citations
TL;DR: The repeated diagonalization techniques used by Eastham to obtain asymptotic results for solutions to linear differential systems are further developed to produce a numerical algorithm for estimating the Titchmarsh-Weyl m -coefficient in the second-order case as discussed by the authors.
Abstract: The repeated diagonalization techniques used by Eastham to obtain asymptotic results for solutions to linear differential systems are further developed to produce a numerical algorithm for estimating the Titchmarsh-Weyl m -coefficient in the second-order case. These analytic results have been exploited to produce a computer code (RDML1) to generate these solutions and to obtain precise global error bounds.
13Â citations
TL;DR: In this article, the Hardy Everitt Littlewood and Polya inequality using numerical techniques is presented and analyzed further, and new techniques are used to integrate the highly oscillatory solutions that restricted the range of problems covered in earlier publications.
Abstract: Recent work on the Hardy Everitt Littlewood and Polya (HELP) inequality using numerical techniques is presented and analysed further. New techniques are used to integrate the highly oscillatory solutions that restricted the range of problems covered in earlier publications.
4Â citations
01 Jan 1994
TL;DR: In this article, the ideas and results obtained so far are summarized and presented in an expository manner, and basic results are discussed to show how these basic results can be applied to various types of $N$-body Schrodinger operators.
Abstract: In Evans–Lewis [5] and Evans–Lewis–Saitō [6], [7], [8], [9] we have been discussing conditions for the finiteness and for the infiniteness of bound states of Schrodinger-type operators using geometric methods. Here the ideas and results obtained so far are summarized and presented in an expository manner. These bound states correspond to eigenvalues below the essential spectrum of the operator. After basic results are presented, Schrodinger operators of atomic type will be discussed to show how these basic results can be applied to various types of $N$-body Schrodinger operators.