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The Y transforms and allied pseudo-differential operators
In this paper, we introduce and study the two versions of Y-transform, which are adjoint to each other. Certain differential operators associated...
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Boundedness of the differential transforms for the generalized Poisson operators generated by Laplacian
In this paper, we consider the boundedness of the differential transforms for the generalized Poisson operators associated with the Laplace operator
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Integral transforms suitable for solving fractional differential equations
The purpose of this article is to obtain appropriate tools for solving fractional differential equations that are flexible enough to adapt to...
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On Applications of Integral Transforms Composition Method
AbstractThe purpose of this paper is to address questions related to transmutation theory and applications of the integral transforms composition...
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Ray Transforms of the Moments of Planar Tensor Fields
AbstractThe paper considers ray transforms of the moments of symmetric tensor fields of arbitrary rank given in the unit disk. The basic geometric...
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A pair of Barut-Girardello type transforms and allied pseudo-differential operators
The main objective of this paper is to generalize the Barut-Girardello transform (BG-transform) in two different ways as a pair of Barut-Girardello...
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Integral Equations and Integral Transforms
This comprehensive textbook on linear integral equations and integral transforms is aimed at senior undergraduate and graduate students of...
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Further Quaternion Integral Transforms
As may be expected the modification of the QFT to a localized QWT only formed the beginning of a rich field of novel quaternionic integral...
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Inversion Problem for Radon Transforms Defined on Pseudoconvex Sets
AbstractSome questions concerning the inversion of the classical and generalized integral Radon transforms are discussed. The main issue is to...
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Laplace Transforms
The Laplace transform is a fundamental tool for solving ordinary differential equations with constant coefficients. This chapter presents the main...
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Weighted Pullback Transforms on Riemann Surfaces
In this paper, using properties of the conditional expectation operators we give an explicit formula for the adjoint of a bounded weighted pullback...
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Quaternion Hyperbolic Fourier Transforms and Uncertainty Principles
The present study introduces the two-sided and right-sided Quaternion Hyperbolic Fourier Transforms (QHFTs) for analyzing two-dimensional...
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Transforming Radical Differential Equations to Algebraic Differential Equations
In this paper, we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with...
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Legendre functions, related Lebedev–Skalskaya transforms pairs and associated operators
In this paper, a brief study is made on the Legendre function related to the Lebedev–Skalskaya transform (LSL-transform) pairs. Some preliminary...
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Quaternionic Slice Regular Functions and Quaternionic Laplace Transforms
The functions studied in the paper are the quaternion-valued functions of a quaternionic variable. It is shown that the left slice regular functions...
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Multiscale transforms for signals on simplicial complexes
Our previous multiscale graph basis dictionaries/graph signal transforms—Generalized Haar-Walsh Transform (GHWT); Hierarchical Graph Laplacian Eigen...
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Reconstruction of Three-Dimensional Vector Fields Based on Values of Normal, Longitudinal, and Weighted Radon Transforms
AbstractThe paper considers the vector tomography problem of reconstructing a three-dimensional vector field based on the values of unweighted...
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Remarks on asymptotic isometric embeddings of conic transforms for torus actions
Consider a Hodge manifold and assume that a torus acts on it in a Hamiltonian and holomorphic manner and that this action linearizes on a given...
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Integral Transforms and Special Functions
This chapter provides the essential mathematical tools to be used in the subsequent chapters, and is intended to make the book as self-contained as...
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New Gaussian Riesz transforms on variable Lebesgue spaces
We give sufficient conditions on the exponent p : ℝ d → [1, ∞) for the boundedness of the non-centered Gaussian maximal function on variable Lebesgue...