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Mkhitar Djrbashian and His Contribution to Fractional Calculus
This survey paper is devoted to the description of the results by M.M. Djrbashian related to the modern theory of Fractional Calculus. M.M....
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Modified Hardy and Hardy–Littlewood Fractional Operators in Morrey–Herz Spaces and Their Commutators in Weighted Spaces
In this paper, we obtain sufficient conditions of the boundedness of modified fractional Hardy–Littlewood and Hardy operators acting from one...
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The Hilbert Transform for Dunkl Differential Operators Associated to the Reflection Group ℤ2
The aim of this paper is to introduce the Dunkl—Hilbert transform H k , with k ≥ 0, induced by the Dunkl differential operator and associated with the...
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Short time coupled fractional fourier transform and the uncertainty principle
In this paper, we introduce a short-time coupled fractional Fourier transform ( scfrft ) using the kernel of the coupled fractional Fourier transform ( cfrft...
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A Variation of Lp Uncertainty Principles in Weinstein Setting
The Weinstein operator has several applications in pure and applied Mathematics especially in Fluid Mechanics and satisfies some uncertainty...
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Boundedness of the Hilbert Transform in Besov Spaces
Boundedness conditions are found for the Hilbert transform H in Besov spaces with Muckenhoupt weights. The operator H in this situation acts on...
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Some Characterization of Herz and Herz-Type Hardy Spaces for the Dunkl Operator
In this work, new characterizations of Herz and Herz-type Hardy spaces associated with the Dunkl operator on the real line are introduced.
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The Integral Transform of N.I. Akhiezer
We study the integral transform which appeared in a different form in Akhiezer’s textbook “Lectures on Integral Transforms”.
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Theorems on Some Families of Fractional Differential Equations and Their Applications
We use the Laplace transform method to solve certain families of fractional order differential equations. Fractional derivatives that appear in these...
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Spectra of rational orthonormal systems
We use the Weyl correspondence approach to investigate the spectral operators of the Laguerre and the Kautz systems. We show that the basic functions...
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Boundary Values of Discrete Monogenic Functions over Bounded Domains in \( \mathbb{R}^3 \)
In this paper we are going to study boundary values for discrete monogenic functions over bounded spatial domains. After establishing the discrete...
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Inverse Problems for Arbitrary Order Integral and Integro-Differential Operators
Inverse spectral problems are studied for arbitrary order integral and integro-differential operators. We develop a method and algorithms for...
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Hardy’s Inequalities for the Heisenberg Group
This article presents two types of Hardy’s inequalities for the Heisenberg group. The proofs are mainly based on estimates of the Fourier transform...
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Lebedev type index transforms with the squares of the associated Legendre functions
The classical Lebedev index transform [
3 ] involving squares and products of the Legendre functions is generalized on the associated Legendre... -
Lower Bounds for Truncated Fourier and Laplace Transforms
We prove sharp stability estimates for the Truncated Laplace Transform and Truncated Fourier Transform. The argument combines an approach recently...
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Numerical Solutions for Systems of Nonlinear Fractional Ordinary Differential Equations Using the FNDM
A new technique has been developed for analytical solutions of fractional order nonlinear ODE system. We propose a reliable method called the...
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The Ridgelet Transform and Quasiasymptotic Behavior of Distributions
We characterize the quasiasymptotic behavior of distributions in terms of a Tauberian theorem for ridgelet transforms.
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Sampling Formulas for Groups of Operators in Banach Spaces
We extend some results about sampling of entire functions of exponential type to Banach spaces. By using the generator D of a one-parameter group e tD ...