共查询到20条相似文献，搜索用时 14 毫秒
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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
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《Integral Transforms and Special Functions》2012,23(4):279-282
Some results are given about the inverse of the Hankel transform. 相似文献
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In this paper, we define the quadratic-phase Fourier wavelet transform (QPFWT) and discuss its basic properties including convolution for QPFWT. Further, inversion formula and the Parseval relation of QPFWT are also discussed. Continuity of QPFWT on some function spaces are studied. Moreover, some applications of quadratic-phase Fourier transform (QPFT) to solve the boundary value problems of generalized partial differential equations. 相似文献
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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
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《Integral Transforms and Special Functions》2012,23(1):1-16
Hankel translations and Hankel convolutions of three different orders are defined. Their properties are investigated. An application to the Bessel differential operator is given. 相似文献
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Fractional cosine transform (FRCT) and fractional sine transform (FRST), which are closely related to the fractional Fourier transform (FRFT), are useful mathematical and optical tool for signal processing. Many properties for these transforms are well investigated, but the convolution theorems are still to be determined. In this paper, we derive convolution theorems for the fractional cosine transform (FRCT) and fractional sine transform (FRST) based on the four novel convolution operations. And then, a potential application for these two transforms on designing multiplicative filter is presented. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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Tempered fractional Brownian motion is obtained when the power law kernel in the moving average representation of a fractional Brownian motion is multiplied by an exponential tempering factor. This paper develops the theory of stochastic integrals for tempered fractional Brownian motion. Along the way, we develop some basic results on tempered fractional calculus. 相似文献
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In this work, we have introduced a pair of linear canonical Hankel transformations and investigated some of its properties on Zemanian-type spaces. Moreover two versions of pseudo-differential operator associated with canonical Hankel transformations are defined and discussed its integral representation. 相似文献
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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
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《Integral Transforms and Special Functions》2012,23(5):315-323
The main objective of this paper is to study the continuous Bessel wavelet transformation and its inversion formula, and the Parseval relation using the theory of the Hankel convolution. A relation between the Bessel wavelet transformation and the Hankel–Hausdorff operator is established. 相似文献
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In this present article, we study the fractional Hankel transform and its inverse on certain Gel'fand‐Shilov spaces of type S. The continuous fractional wavelet transform is defined involving the fractional Hankel transform. The continuity of fractional Hankel wavelet transform is discussed on Gel'fand‐Shilov spaces of type S. This article goes further to discuss the continuity property of fractional Hankel transform and fractional Hankel wavelet transform on the ultradifferentiable function spaces. 相似文献
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Ram Shankar Pathak 《Applicable analysis》2013,92(10):1223-1236
A class of pseudo-differential operators (p.d.o.'s) associated with the general Fourier kernel studied by Hardy and Titchmarsh is defined. A symbol class T m is introduced. It is shown that the p.d.o.'s associated with the symbol are continuous linear mappings of the Braaksma and Schuitman space T(λ,μ) into itself. An integral representation of p.d.o. is obtained. Some special forms of the symbol are considered. It is shown that these p.d.o.'s and their products are bounded in certain Sobolev type space. 相似文献
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《Integral Transforms and Special Functions》2012,23(6):465-477
The pseudo-differential operator (p.d.o.) h μ, a associated with the Bessel operator involving the symbol a(x, y) whose derivatives satisfy certain growth conditions depending on some increasing sequences is studied on certain Gevrey spaces. The p.d.o. h μ, a on Hankel translation τ and Hankel convolution of Gevrey functions is a continuous linear mapping into another Gevrey space. 相似文献
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Cesar Enrique Torres Ledesm Ziheng Zhang Amado Mendez 《Journal of Applied Analysis & Computation》2019,9(6):2436-2453
We study the existence of solutions for the following fractional Hamiltonian systems$$left{ begin{array}{ll} - _tD^{alpha}_{infty}(_{-infty}D^{alpha}_{t}u(t))-lambda L(t)u(t)+nabla W(t,u(t))=0,[0.1cm] uin H^{alpha}(mathbb{R},mathbb{R}^n), end{array}right. ~~~~~~~~~~~~~~~~~(FHS)_lambda$$where $alphain (1/2,1)$, $tin mathbb{R}$, $uin mathbb{R}^n$, $lambda>0$ is a parameter, $Lin C(mathbb{R},mathbb{R}^{n^2})$ is a symmetric matrix, $Win C^1(mathbb{R} times mathbb{R}^n,mathbb{R})$. Assuming that$L(t)$ is a positive semi-definite symmetric matrix, that is, $L(t)equiv 0$ is allowed to occur in some finite interval $T$ of $mathbb{R}$,$W(t,u)$ satisfies some superquadratic conditions weaker than Ambrosetti-Rabinowitz condition, we show that (FHS)$_lambda$ has a solution which vanishes on$mathbb{R}setminus T$ as $lambda to infty$, and converges to some $tilde{u}in H^{alpha}(R, R^n)$. Here, $tilde{u}in E_{0}^{alpha}$ is a solutionof the Dirichlet BVP for fractional systems on the finite interval $T$. Our results are new and improve recent results in the literature even in the case $alpha =1$. 相似文献
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《Integral Transforms and Special Functions》2012,23(7):479-486
In this paper, we introduce the Hankel transform as a continuous linear map from one space of Boehmian into another and study its operational properties. 相似文献