Basic analog of Fourier series on a $q$-quadratic grid
Joaquin Bustoz,Sergei K. Suslov +1 more
TLDR
In this paper, the authors prove orthogonality relations for some analogs of trigonometric functions on a g-quadratic grid and introduce the corresponding g-Fourier series.Abstract:
We prove orthogonality relations for some analogs of trigonometric functions on a g-quadratic grid and introduce the corresponding g-Fourier series. We also discuss several other properties of this basic trigonometric system and the g-Fourier series.read more
Citations
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Journal ArticleDOI
Basic Sturm?Liouville problems
TL;DR: In this article, a self-adjoint q-difference operator in a Hilbert space is proposed and the set of eigenfunctions is shown to be a complete orthogonal set in the Hilbert space.
Book ChapterDOI
q -Difference Equations
TL;DR: In this article, Mansour et al. presented proofs of the existence and uniqueness of the solutions of first order systems of q-difference equations in a neighborhood of a point a, \(a \geq 0\).
Journal ArticleDOI
Basic Analog of Fourier Series on a q-Linear Grid
J. Bustoz,José Luís Cardoso +1 more
TL;DR: The q-linear initial value problem δf(x)δx= λf (x),f(0)=1, has two entire functions Cq (z) and Sq(z) as linearly independent solutions.
Journal ArticleDOI
THE ROOTS OF THE THIRD JACKSON q-BESSEL FUNCTION
TL;DR: In this article, the authors derived analytic bounds for the zeros of the third Jackson -Bessel function J v ( 3 ) ( z ; q ) for the case where q is the number of zeros.
Journal ArticleDOI
Introductory Real Analysis. By A. N. Kolmogorov and S. V. Fomin, translated by Richard A. Silverman. Pp. xii, 403. (Prentice-Hall Inc.)
TL;DR: In this article, the authors introduce real analysis for real analysis in the context of real data analysis, and propose a real analysis framework for real data collection and analysis, using real data.
References
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A treatise on the theory of Bessel functions
TL;DR: The tabulation of Bessel functions can be found in this paper, where the authors present a comprehensive survey of the Bessel coefficients before and after 1826, as well as their extensions.
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A Course of Modern Analysis
TL;DR: The volume now gives a somewhat exhaustive account of the various ramifications of the subject, which are set out in an attractive manner and should become indispensable, not only as a textbook for advanced students, but as a work of reference to those whose aim is to extend the knowledge of analysis.
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Basic Hypergeometric Series
George Gasper,Mizan Rahman +1 more
TL;DR: In this article, the Askey-Wilson q-beta integral and some associated formulas were used to generate bilinear generating functions for basic orthogonal polynomials.
Book
Theory of linear operators in Hilbert space
N. I. Akhiezer,I. M. Glazman +1 more
TL;DR: In this article, the main properties of bounded and unbounded operators, adjoint operators, symmetric and self-adjoint operators in hilbert spaces are discussed, as well as the stability of self-jointness under small perturbations.