共查询到20条相似文献,搜索用时 31 毫秒
1.
Kanailal Mahato 《Integral Transforms and Special Functions》2017,28(11):789-800
This article is concerned with the study of the continuity of wavelet transform involving fractional Hankel transform on certain function spaces. The n-dimensional boundedness property of the fractional wavelet transform is also discussed on Sobolev type space. Particular cases are also considered. 相似文献
2.
Gelfand–Shilov spaces are spaces of entire functions defined in terms of a rate of growth in one direction and a concomitant rate of decay in an orthogonal direction. Gelfand and Shilov proved that the Fourier transform is an isomorphism among certain of these spaces. In this article we consider mapping properties of fractional Fourier transforms on Gelfand–Shilov spaces. Just as the Fourier transform corresponds to rotation through a right angle in the phase plane, fractional Fourier transforms correspond to rotations through intermediate angles. Therefore, the aim of fractional Fourier estimates is to set up a correspondence between growth properties in the complex plane versus decay properties in phase space. 相似文献
3.
The main goal of this paper is to study about the continuous as well as discrete wavelet transform in terms of linear canonical Hankel transform (LCH‐transform) and discuss some of its basic properties. Parseval's relation and reconstruction formula of continuous linear canonical Hankel wavelet transform (CLCH‐wavelet transform) is obtained. Moreover, semidiscrete and discrete LCH‐wavelet transform are also discussed. 相似文献
4.
On the Sobolev boundedness results of the product of pseudo-differential operators involving a couple of fractional Hankel transforms
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This article is concerned with the study of pseudo-differential operators associated with fractional Hankel transform. The product of two fractional pseudo-differential operators is defined and investigated its basic properties on some function space. It is shown that the pseudo-differential operators and their products are bounded in Sobolev type spaces. Particular cases are discussed. 相似文献
5.
In this paper, we investigate the long-range dependence of fractional Levy processes on Gel’fand triple and construct stochastic integral with respect to fractional Levy processes for a class of deterministic integrands. 相似文献
6.
Vladislav V. Kravchenko 《Mathematical Methods in the Applied Sciences》2019,42(4):1321-1327
A method for solving the inverse scattering problem on the line is proposed. It is based on a Fourier‐Laguerre series representation of the integral transmutation kernel. Substitution of the representation into the Gel'fand‐Levitan‐Marchenko equation leads to a linear algebraic system of equations and consequently to a simple algorithm for recovering the potential. 相似文献
7.
M.I. Isaev 《Applicable analysis》2013,92(11):2262-2274
We give an instability estimate for the Gel'fand inverse boundary value problem at high energies. Our instability estimate shows an optimality of several important preceding stability results on inverse problems of such a type. 相似文献
8.
Hari M. Srivastava Komal Khatterwani S. K. Upadhyay 《Mathematical Methods in the Applied Sciences》2019,42(9):3103-3122
In the present paper, a fractional wavelet transform of real order α is introduced, and various useful properties and results are derived for it. These include (for example) Perseval's formula and inversion formula for the fractional wavelet transform. Multiresolution analysis and orthonormal fractional wavelets associated with the fractional wavelet transform are studied systematically. Fractional Fourier transforms of the Mexican hat wavelet for different values of the order α are compared with the classical Fourier transform graphically, and various remarkable observations are presented. A comparative study of the various results, which we have presented in this paper, is also represented graphically. 相似文献
9.
《代数通讯》2013,41(4):1519-1530
Abstract Let G = GL n (q) be the general linear group over a finite field 𝔽 q with q elements. We call a Gel'fand–Graev module to be the module which affords the Gel'fand–Graev character defined in Definition I.1. It is known that every cuspidal module of G is isomorphic to a (unique) direct summand of a Gel'fand–Graev module. In this article, we investigate a certain endomorphism so that each irreducible cuspidal module is contained in a certain eigenspace corresponding to the cuspidal character. Furthermore, we determine the eigenvalue of that endomorphism by using character theory of finite general linear group. 相似文献
10.
Aline Bonami Sandrine Grellier Mohammad Kacim 《Transactions of the American Mathematical Society》2008,360(3):1377-1390
We extend to multilinear Hankel operators the fact that some truncations of bounded Hankel operators are still bounded. We prove and use a continuity property of bilinear Hilbert transforms on products of Lipschitz spaces and Hardy spaces.
11.
Briceyda B. Delgado Kira V. Khmelnytskaya Vladislav V. Kravchenko 《Mathematical Methods in the Applied Sciences》2019,42(18):7359-7366
The inverse Sturm‐Liouville problem on a half‐line is considered. With the aid of a Fourier‐Legendre series representation of the transmutation integral kernel and the Gel'fand‐Levitan equation, the numerical solution of the problem is reduced to a system of linear algebraic equations. The potential q is recovered from the first coefficient of the Fourier‐Legendre series. The resulting numerical method is direct and simple. The results of the numerical experiments are presented. 相似文献
12.
《Journal of Complexity》2002,18(3):815-832
The purpose of the present paper is to consider some weak asymptotic problems concerning the infinite-dimensional Kolmogorov widths, the infinite-dimensional linear widths, the infinite-dimensional Gel'fand widths and optimal recovery in Besov space. It is obvious to be found that the results obtained and methods used in Besov space are easily generalized, and hence in this paper these results in an extension of Besov spaces on Rd are stated and proved. Meantime, the representation theorem and approximation of these spaces by polynomial splines are discussed. 相似文献
13.
C. Baccar 《Integral Transforms and Special Functions》2016,27(6):413-429
The aim of this paper is to prove Heisenberg-type uncertainty principles for the continuous Hankel wavelet transform. We also analyse the concentration of this transform on sets of finite measure. Benedicks-type uncertainty principle is given. 相似文献
14.
Using the theory of Hankel convolution, continuous and discrete Bessel wavelet transforms are defined. Certain boundedness results and inversion formula for the continuous Bessel wavelet transform are obtained. Important properties of the discrete Bessel wavelet transform are given. 相似文献
15.
《Journal of Algebra》2006,295(1):247-268
We describe simple finitely generated associative conformal algebras of Gel'fand–Kirillov dimension one. 相似文献
16.
Shapiro’s dispersion and Umbrella theorems are proved for the continuous Hankel wavelet transform. As a side results, we extend local uncertainty principles for set of finite measure to the latter transform. 相似文献
17.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1999,328(11):969-972
We define a sequence of generalized Radon transforms, which are intertwining operators for natural representations associated to Gel'fand spaces for the symmetric group Sn. This sequence enables us to decompose in a recursive way these natural representations and to compute explicitly the associate spherical functions. We prove analogous results for a sequence of generalized Radon transforms between natural representations for the general linear group GL(n,q), which are a q-analogue of the preceding ones. 相似文献
18.
Elina Shishkina 《Mathematical Methods in the Applied Sciences》2019,42(15):5060-5071
The paper is devoted to the study of the fractional integral operator, which is a negative real power of the singular wave operator generated by Bessel operator using weighted generalized functions. We give conditions for this operator to be bounded in appropriate spaces, obtain formula for the Hankel transform of this operator, and get formula of connection between this operator and natural degree of singular wave operator generated by Bessel operator. 相似文献
19.
In this paper, diameters in the sense of A. N. Kolmogorov are found for the class of 2π-periodic functions W(r)Hω in the space L, that is, d2n-1(W(r)Hω,L), where ω(t) is an upper-convex regular modulus of continuity (r, n=1, 2, ...). An estimate from below is found for diameters in the sense of I. M. Gel'fand, that is, d2n-!(W(r)Hω,L). 相似文献
20.
By expressing the Dunkl transform of order α of a function f in terms of the Hankel transforms of orders α and α + 1 of even and odd parts of f, respectively, we show that a considerable part of harmonic analysis of the Dunkl transform on the real line may be reduced to known results for the Hankel transform. In particular, defining the modified Dunkl transform and then considering the Dunkl transplantation operator we transfer known multiplier results for the Hankel transform to the Dunkl transform setting. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献