共查询到20条相似文献,搜索用时 31 毫秒
1.
Lazhar Dhaouadi 《Integral Transforms and Special Functions》2015,26(2):102-117
A new formulation of the Graf-type addition formula related to the third Jackson q-Bessel function gives a solution for the problem of the positivity of the generalized q-translation operator associated with the q-Hankel transform. Next some applications in q-theory are treated, for instance the relationship between the q-Bessel- positive and negative-definite functions. We also show how the positivity of the q-Bessel translation operator plays a central role in q-Fourier analysis, namely in the study of Markov operators in the q-context. The paper concludes with the nonnegative product linearization of the q?2-Lommel polynomials. 相似文献
2.
This paper deals with firstly the analogue of the Bochner theorem related to q-Bessel function of the third kind and secondly we give a new proof of the analogue of Bernstein’s theorem via the q-Taylor formula. Finally we show that the q-Bessel positive definite and D
q
-completely monotonic functions are linked. 相似文献
3.
Néji Bettaibi Fethi Bouzeffour 《Journal of Mathematical Analysis and Applications》2008,342(2):1203-1219
This paper is devoted to the study of some q-harmonic analysis related to the third q-Bessel function of order zero. We establish a product formula leading to a q-translation with some positive kernel. As an application, we provide a q-analogue of the continuous wavelet transform related to this harmonic analysis. 相似文献
4.
Meryam Ben Said Khaled Mehrez Jamel El Kamel 《Journal of Difference Equations and Applications》2018,24(1):48-58
Intrinsic inequalities involving Turán-type inequalities for some q-special functions are established. A special interest is granted to q-Dunkl kernel. The results presented here would provide extensions of those given in the classical case. 相似文献
5.
We give a group theory interpretation of the three types of q-Bessel functions. We consider a family of quantum Lorentz groups and a family of quantum Lobachevsky spaces. For three values of the parameter of the quantum Lobachevsky space, the Casimir operators correspond to the two-body relativistic open Toda-chain Hamiltonians whose eigenfunctions are the modified q-Bessel functions of the three types. We construct the principal series of unitary irreducible representations of the quantum Lorentz groups. Special matrix elements in the irreducible spaces given by the q-Macdonald functions are the wave functions of the two-body relativistic open Toda chain. We obtain integral representations for these functions. 相似文献
6.
H. T. Koelink 《Journal of Approximation Theory》1999,96(2):345
The basic Lommel polynomials associated to the11q-Bessel function and the Jacksonq-Bessel functions are considered as orthogonal polynomials inqν, whereνis the order of the corresponding basic Bessel functions. The corresponding moment problems are both indeterminate and determinate depending on a parameter. Using techniques of Chihara and Maki we derive an explicit orthogonality measure, which is discrete and unbounded. For the indeterminate moment problem this measure is N-extremal. Some results on the zeros of the basic Bessel functions, both as functions of the order and of the argument are obtained. Precise asymptotic behaviour of the zeros of the11q-Bessel function is obtained. 相似文献
7.
Using a new formulation of Graf’s addition formula related to the third Jackson q-Bessel function, we study the positivity of the generalized q-translation operator associated with the q-Hankel transform. 相似文献
8.
In this article we prove that the basic finite Hankel transform whose kernel is the third-type Jackson q-Bessel function has only infinitely many real and simple zeros, provided that q satisfies a condition additional to the standard one. We also study the asymptotic behavior of the zeros. The obtained results are applied to investigate the zeros of q-Bessel functions as well as the zeros of q-trigonometric functions. A basic analog of a theorem of G. Pólya (1918) on the zeros of sine and cosine transformations is also given. 相似文献
9.
(About Jackson q-Bessel functions)Laplace transform allows to resolve differential equations in the neighborhood of an irregular singular point. The purpose of the article is to study how to apply a basic Borel–Laplace transformation to q-difference equations satisfied by the q-Bessel functions of F.H. Jackson. Connection matrices are obtained between solutions at the origin and solutions at infinity. 相似文献
10.
Wolter Groenevelt 《The Ramanujan Journal》2018,47(2):317-337
The 6j-symbols for representations of the q-deformed algebra of polynomials on \(\mathrm {SU}(2)\) are given by Jackson’s third q-Bessel functions. This interpretation leads to several summation identities for the q-Bessel functions. Multivariate q-Bessel functions are defined, which are shown to be limit cases of multivariate Askey–Wilson polynomials. The multivariate q-Bessel functions occur as 3nj-symbols. 相似文献
11.
We derive representations for certain entire q-functions and apply our technique to the Ramanujan entire function (or q-Airy function) and q-Bessel functions. This is used to show that the asymptotic series of the large zeros of the Ramanujan entire function and similar functions are also convergent series. The idea is to show that the zeros of the functions under consideration satisfy a nonlinear integral equation. 相似文献
12.
We give sufficient conditions which guarantee that the finite q-Hankel transforms have only real zeros which satisfy some asymptotic relations. The study is carried out using two different techniques. The first is by a use of Rouché's theorem and the other is by applying a theorem of Hurwitz and Biehler. In every study further restrictions are imposed on q(0,1). We compare the results via some interesting applications involving second and third q-Bessel functions as well as q-trigonometric functions. 相似文献
13.
In this paper, we consider the fractional q-integral with variable lower limit of integration. We prove the semigroup property of these integrals, and a formula of Leibniz type. Finally, we evaluate fractional q-integrals of some functions. The consideration of q-exponential function in that sense leads to q-analogs of Mittag-Leffier function. 相似文献
14.
We study Fourier–Bessel series on a q-linear grid, defined as expansions in complete q-orthogonal systems constructed with the third Jackson q-Bessel function, and obtain sufficient conditions for uniform convergence. The convergence results are illustrated with specific examples of expansions in q-Fourier–Bessel series.
相似文献15.
Predrag M. Rajković Sladjana D. Marinković Miomir S. Stanković 《The Ramanujan Journal》2006,12(2):245-255
We construct the sequence of orthogonal polynomials with respect to an inner product which is defined by q-integrals over a collection of intervals in the complex plane. We prove that they are connected with little q-Jacobi polynomials. For such polynomials we discuss a few representations, a recurrence relation, a difference equation,
a Rodrigues-type formula and a generating function.
2000 Mathematics Subject Classification Primary—33D45, 42C05 相似文献
16.
Hidekazu Tanaka 《The Ramanujan Journal》2011,24(1):33-60
Kurokawa introduced q-multiple gamma functions and q-multiple sine functions. We show that the Appell’s O-function is expressed via the q-multiple gamma function. We also give some applications of this result. For example, we obtain a formula for the “Stirling
modular form” and calculate special values of the q-multiple sine function. Moreover, we give some formulas of Eisenstein series and double cotangent functions and its generalization.
Then the former gives an infinite product expression of the double sine function explicitly and a result of Kurokawa. 相似文献
17.
Laurent polynomials related to the Hahn-Extonq-Bessel function, which areq-analogues of the Lommel polynomials, have been introduced by Koelink and Swarttouw. The explicit strong moment functional with respect to which the Laurentq-Lommel polynomials are orthogonal is given. The strong moment functional gives rise to two positive definite moment functionals. For the corresponding sets of orthogonal polynomials, the orthogonality measure is determined using the three-term recurrence relation as a starting point. The relation between Chebyshev polynomials of the second kind and the Laurentq-Lommel polynomials and related functions is used to obtain estimates for the latter. 相似文献
18.
Ruiming Zhang 《Advances in Mathematics》2008,217(4):1588-1613
In this work we study the chaotic and periodic asymptotics for the confluent basic hypergeometric series. For a fixed q∈(0,1), the asymptotics for Euler's q-exponential, q-Gamma function Γq(x), q-Airy function of K. Kajiwara, T. Masuda, M. Noumi, Y. Ohta and Y. Yamada, Ramanujan function (q-Airy function), Jackson's q-Bessel function of second kind, Ismail-Masson orthogonal polynomials (q−1-Hermite polynomials), Stieltjes-Wigert polynomials, q-Laguerre polynomials could be derived as special cases. 相似文献
19.
Howard S. Cohl Jessica E. Hirtenstein Hans Volkmer 《Integral Transforms and Special Functions》2016,27(10):767-774
In 1946, Magnus presented an addition theorem for the confluent hypergeometric function of the second kind U with argument x+y expressed as an integral of a product of two U's, one with argument x and another with argument y. We take advantage of recently obtained asymptotics for U with large complex first parameter to determine a domain of convergence for Magnus' result. Using well-known specializations of U, we obtain corresponding integral addition theorems with precise domains of convergence for modified parabolic cylinder functions, and Hankel, Macdonald, and Bessel functions of the first and second kind with order zero and one. 相似文献
20.
Jeroen Noels 《Algebras and Representation Theory》2004,7(2):101-138
In a previous article we proposed an algebraic setting in which to perform harmonic analysis on noncompact, nondiscrete quantum groups and in particular, on quantum E(2). In the present paper we shall explicitly construct Fourier transforms between quantum E(2) and its Pontryagin dual, involving Hahn—Exton q-Bessel functions as kernel, prove Plancherel and inversion formulas, etc. We also develop a theory of q-Hankel transformation of entire functions, based on the definition proposed by Koornwinder and Swarttouw. 相似文献