共查询到20条相似文献，搜索用时 15 毫秒
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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
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《Integral Transforms and Special Functions》2012,23(6):481-496
The aim of this paper is to prove a version of Heisenberg's uncertainty inequality for the windowed Hankel transform. As a side results, we extend some others uncertainty principles about sets of finite measure to the windowed Hankel transform which are valid for the windowed Fourier transform. 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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Emna Tefjeni 《Integral Transforms and Special Functions》2020,31(8):669-684
ABSTRACT In this paper, we present some new elements of harmonic analysis related to the right-sided multivariate continuous quaternion wavelet transform. The main objective of this article is to introduce the concept of the right-sided multivariate continuous quaternion wavelet transform and investigate its different properties using the machinery of multivariate quaternion Fourier transform. Last, we have proven a number of uncertainty principles for the right-sided multivariate continuous quaternion wavelet transform. 相似文献
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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
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Juan Miguel Medina Bruno Cernuschi-Frías 《Numerical Functional Analysis & Optimization》2018,39(1):87-99
We shall prove some simultaneous localization or concentration inequalities for the continuous wavelet transform. We will also show that simultaneous localization in the scale-time(space) is impossible, in the sense that the scale sections of the support of wavelet transform of a nonnull Lp-function can not have finite Lebesgue measure. Finally, some properties of the support of continuous wavelet transform of band-limited functions are studied. 相似文献
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《Integral Transforms and Special Functions》2012,23(6):470-484
The aim of this paper is to establish an analogue of Logvinenko–Sereda's theorem for the Fourier–Bessel transform (or Hankel transform) ℱα of order α>−½. Roughly speaking, if we denote by PWα(b) the Paley–Wiener space of L 2-functions with the Fourier–Bessel transform supported in [0, b], then we show that the restriction map f→f|Ω is essentially invertible on PWα(b) if and only if Ω is sufficiently dense. Moreover, we give an estimate of the norm of the inverse map. As a side result, we prove a Bernstein-type inequality for the Fourier–Bessel transform. 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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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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《Integral Transforms and Special Functions》2012,23(9):703-712
The Price uncertainty principle is proved for the Hankel transform. 相似文献
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《Integral Transforms and Special Functions》2012,23(6):491-501
The aim of this paper is to prove new uncertainty principles for the Dunkl transform. More precisely, we show a variation on Heisenberg's uncertainty inequality, the local uncertainty principle and Donoho–Stark's uncertainty principle. 相似文献
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《Integral Transforms and Special Functions》2012,23(5):327-332
In S.E. Trione and S. Molina, The n-dimensional Hankel transform and complex powers of Bessel operator, to appear in Integral Transforms and Spec. Funct. we study a version of the n-dimensional Hankel transform h μ for μ=(μ1, …, μ n )∈ℝ n and μ i ≥−1/2 for all i. In this paper, we extend the n-dimensional Hankel transform to arbitrary values of μ∈ℝ n . Moreover, we obtain some results for the inverse of this extension. 相似文献
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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
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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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《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