منابع مشابه
Szegö on Jacobi Polynomials
One of the interesting features in the development of analysis in the twentieth century is the remarkable growth, in various directions, of the theory of orthogonal functions. Two brilliant achievements on the threshold of this century—Fejér's paper on Fourier series and Fredholm's papers on integral equations—have been acting as a powerful inspiring source of attraction, inviting analysts to d...
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We study a sequence of polynomials orthogonal with respect to a family weights w(x) := w(x, t) = e x(1− x) , t ≥ 0, over [−1, 1]. If t = 0, this reduces to a shifted Jacobi weight. Our ladder operator formalism and the associated compatibility conditions give an easy determination of the recurrence coefficients. For t > 0, the deformation term e−t/x induces an infinitely strong zero at x = 0. T...
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The property that a Jacobi matrix is reflectionless is usually characterized either in terms of Weyl mfunctions or the vanishing of the real part of the boundary values of the diagonal matrix elements of the resolvent. We introduce a characterization in terms of stationary scattering theory (the vanishing of the reflection coefficients) and prove that this characterization is equivalent to the ...
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ژورنال
عنوان ژورنال: Ain Shams Engineering Journal
سال: 2013
ISSN: 2090-4479
DOI: 10.1016/j.asej.2012.06.003