A Singular Convolution Equation In The Space Of Distributions II
A singular convolution equation in the space of distribution. II.
A system of partial differential equations with fractional derivatives.
A uniqueness theorem for Boehmians of analytic type.
Abelian theorem for the Stieltjes transform of distributions.
Abelian Theorems for Distributional H-Transform.
Abelian theorems for transformable Boehmians.
Abelian theorems for Whittaker transforms.
An extension of distributional wavelet transform
We construct a new Boehmian space containing the space 𝓢̃'(ℝⁿ×ℝ₊) and define the extended wavelet transform 𝓦 of a new Boehmian as a tempered Boehmian. In analogy to the distributional wavelet transform, it is proved that the extended wavelet transform is linear, one-to-one, and continuous with respect to δ-convergence as well as Δ-convergence.
An Inversion Formula for the Distributional H-Transformation.
Analytic implementation of the duals of some spaces of infinitely differentiable functions.
Analytic representation of the distributional finite Hankel transform.
Application of the Quasiasymptotic boundedness of distributions of Wavelet transform
Approximation of Distribution Spaces by Means of Kernel Operators.
Asymptotic behavior of Fourier-Laplace transform
Asymptotic expansion of solutions of Laplace-Beltrami type singular operators
The theory of Mellin analytic functionals with unbounded carrier is developed. The generalized Mellin transform for such functionals is defined and applied to solve the Laplace-Beltrami type singular equations on a hyperbolic space. Then the asymptotic expansion of solutions is found.
Asymptotic Expansions of Schwartz's Distributions
Asymptotics of regular convolution quotients.
Between the Paley-Wiener theorem and the Bochner tube theorem
We present the classical Paley-Wiener-Schwartz theorem [1] on the Laplace transform of a compactly supported distribution in a new framework which arises naturally in the study of the Mellin transformation. In particular, sufficient conditions for a function to be the Mellin (Laplace) transform of a compactly supported distribution are given in the form resembling the Bochner tube theorem [2].
Beurling-Gevrey tempered ultradistributions as boundary values