Results 21 to 30 of about 785,515 (75)
The Abel summation of the Kontorovich-Lebedev integral representation [PDF]
, 2005 A new result on the summation of the Kontorovich–Lebedev integral representation in the sense of Abel mean is ...
Petru A. Cojuhari +3 more
core +2 more sources
Upper bounds and asymptotic expansion for Macdonald's function and the summability of the Kontorovich-Lebedev integrals [PDF]
, 2022 Uniform upper bounds and the asymptotic expansion with an explicit remainder term are established for the Macdonald function $K_{i\tau}(x)$. The results can be applied, for instance, to study the summability of the divergent Kontorovich-Lebedev integrals
Yakubovich, S.
core
Wavelet Transforms for the Kontorovich-Lebedev-Clifford Transform and Their Applications
In this paper, we investigate the continuous wavelet transform within the framework of the convolution theory of the Kontorovich-Lebedev-Clifford transform, We derive the reconstruction formula together with the Plancherel and Parseval relations ...
Abdellatif Akhlidj +2 more
core +1 more source
, 2017 The Pseudo-differential operators (p.d.o.) L (
Akhilesh Prasad, Upain K. Mandal
core +1 more source
New index transforms of the Lebedev-Skalskaya type [PDF]
, 2016 New index transforms, involving the real part of the modified Bessel function of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue spaces ...
Yakubovich, SB
core +1 more source
Distributional Extensions of the Kontorovich–Lebedev and Fourier– Kontorovich–Lebedev Transforms
This paper develops a distributional theory of the KL transform and its two-sided Fourier–Kontorovich–Lebedev (FKF) counterpart. A fundamental distributional inversion identity is established in which a regularized Macdonald kernel converges to the Dirac
Shinde SM
core +1 more source
Time-dependent problems for a wedge via Kontorovich-Lebedev's transform
, 2020 The aim of this paper is to solve a certain type of time-dependent problems for a wedge in terms of the Kontorovich-Lebedev integral. In order to do that we will consider a certain testing-function space for distributions associated with the two ...
N Vieira, S Yakubovich
core
On the Fourier cosine—Kontorovich-Lebedev generalized convolution transforms [PDF]
, 2013 summary:We deal with several classes of integral transformations of the form $$ \label {generalformula} f(x)\rightarrow D\int _{\mathbb R_+^2} \frac 1u ({\rm e}^{-u\cosh (x+v)}+{\rm e}^{-u\cosh (x-v)}) h(u)f(v) {\rm d}u {\rm d} v, $$ where $D$ is an ...
Hong, Nguyen Thanh +2 more
core +1 more source
The Kontorovich–Lebedev (KL) transform, built upon the Macdonald function of purely imaginary order, occupies a central position in the spectral theory of continuous groups and in the analysis of radially symmetric problems on the hyperbolic plane.
V. A. Sharma
core +1 more source
The Kontorovich–Lebedev (KL) transform, defined by integration against the Macdonald function of purely imaginary order, is a classical continuous analogue of the Fourier–Bessel expansion. This paper develops a self-contained account of the operator, its
V. A. Sharma
core +1 more source