Results 1 to 10 of about 785,515 (75)
On the Lebedev transformation in Hardy's spaces
International Journal of Mathematics and Mathematical Sciences, 2004 We establish the inverse Lebedev expansion with respect to parameters and arguments of the modified Bessel functions for an arbitrary function from Hardy's space H2,A, A>0.
Semyon B. Yakubovich
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On a non-self adjoint eigenfunction expansion [PDF]
International Journal of Mathematics and Mathematical Sciences, 1984 This paper develops a formula of inversion for an integral transform similar to that associated with the names of Kontorovich and Lebedev. The kernel involves the Hankel function Hu(1)(kr), in which r varies over a truncated infinite interval a≤r0 and ...
D. Naylor
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A radial version of the Kontorovich-Lebedev transform in the unit ball [PDF]
Opuscula Mathematica, 2011 In this paper we introduce a radial version of the Kontorovich-Lebedev transform in the unit ball. Mapping properties and an inversion formula are proved in \(L_p\)
Semyon B. Yakubovich, Nelson Vieira
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Uncertainty principles for the kontorovich‐lebedev transform [PDF]
Mathematical Modelling and Analysis, 2008 By using classical uncertainty principles for the Fourier transform and composition properties of the Kontorovich‐Lebedev transform, analogs of the Hardy, Beurling, Cowling‐Price, Gelfand‐Shilov and Donoho‐Stark theorems are obtained.
Semyon B. Yakubovich
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Beurling's theorems and inversion formulas for certain index transforms [PDF]
Opuscula Mathematica, 2009 The familiar Beurling theorem (an uncertainty principle), which is known for the Fourier transform pairs, has recently been proved by the author for the Kontorovich-Lebedev transform.
Semyon B. Yakubovich
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On a non-self adjoint expansion formula
International Journal of Mathematics and Mathematical Sciences, 1984 This paper develops a formula of inversion for an integral transform of the kind similar to that associated with the names of Kontorovich and Lebedev except that the kernel involves the Neumann function Yu(kr) and the variable r varies over the infinite ...
D. Naylor
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The Mehler-Fock transform of general order and arbitrary index and its inversion
International Journal of Mathematics and Mathematical Sciences, 1984 An integral transform involving the associated Legendre function of zero order, P−12+iτ(x), x∈[1,∞), as the kernel (considered as a function of τ), is called Mehler-Fock transform. Some generalizations, involving the function P−12+iτμ(x), where the order
Cyril Nasim
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A distribution associated with the Kontorovich-Lebedev transform [PDF]
Opuscula Mathematica, 2006 We show that in a sense of distributions \[\lim_{\varepsilon\to 0+} {1\over \pi^2} \tau\sinh\pi\tau \int_{\varepsilon}^{\infty} K_{i\tau}(y)K_{ix}(y){dy\over y} =\delta(\tau-x),\] where \(\delta\) is the Dirac distribution, \(\tau\), \(x\in\mathbb{R ...
Semyon B. Yakubovich
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A double index transform with a product of Macdonald's functions revisited [PDF]
Opuscula Mathematica, 2009 We prove an inversion theorem for a double index transform, which is associated with the product of Macdonald's functions \(K_{i \tau}(\sqrt{x^2+y^2}-y) K_{i \tau}(\sqrt{x^2+y^2}+y)\), where \((x, y) \in \mathbb{R}_+ \times \mathbb{R}_+\) and \(i \tau ...
Semyon B. Yakubovich
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Applied SciencesA general theory for solving electromagnetic diffraction problems with impenetrable/penetrable wedges immersed in/made of an arbitrary linear (bianistropic) medium is presented.
Vito G. Daniele, Guido Lombardi
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