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Fourier Transform
Separation of variables is a powerful technique for solving some partial differential equations on finite domains. When the domain become infinite...
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Fourier Transform
Fourier transforms of integrable functions defined on the whole real line...
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Fourier Transform II
The Fourier transform offers the possibility to determine particulate solutions of linear differential equations. In this process, a differential...
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Fourier Transform
An integral transform of a function f(x) defined on (a, b) has the form $$I(f)\equiv...
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A sparse approximation for fractional Fourier transform
The paper promotes a new sparse approximation for fractional Fourier transform, which is based on adaptive Fourier decomposition in Hardy-Hilbert...
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Quaternion Fourier Transform
This chapter first focusses on the theoretical foundations of quaternion Fourier transforms. Basically, in the complex Fourier transform the...
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Super-Resolution Reconstruction from Truncated Fourier Transform
We present recent theoretical and numerical results on recovering a compactly supported function v on...
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The fractional Fourier–Jacobi wavelet transform
The main aim of this work is to define the fractional Jacobi translation, the fractional Jacobi convolution and to study the fractional...
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Phase Estimation and quantum Fourier Transform (qFT)
Phase estimation and the quantum Fourier transform (qFT) are the inverse of each other. From a pedagogical point of view, to start the discussion...
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Uncertainty principles of hypercomplex functions for fractional Fourier transform
In the present paper, different uncertainty principles for hypercomplex functions associated with the fractional Fourier transform (FRFT) are...
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Fourier Transform
In Chap. 4 we have seen that Fourier series are used to represent periodic functions (or functions defined on a...
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Octonion Fourier Transform
This short chapter surveys five publications that go beyond the generalization of complex Fourier transforms to quaternions by introducing the...
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On Eigenmeasures Under Fourier Transform
Several classes of tempered measures are characterised that are eigenmeasures of the Fourier transform, the latter viewed as a linear operator on...
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Equations Related to Stochastic Processes: Semigroup Approach and Fourier Transform
The work is devoted to integro-differential equations related to stochastic processes. We study the relationship between differential equations with...
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Fourier Transform I
In Fourier series expansion, we have developed a piecewise continuous and T-periodic function f into a Fourier series and thus decomposed the...
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Generalization of the Fast Fourier Transform with a Constant Structure
AbstractThe widely popular famous fast Cooley–Tukey algorithms for the discrete Fourier transform of mixed radix are presented in two forms:...
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Fractional Fourier transform for space–time algebra-valued functions
The aim of this article is to introduce a fractional space–time Fourier transform (FrSFT) by generalizing the fractional Fourier transform for...
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Fourier-Transform Method for Partial Differential Equations. Part 2. Existence and Uniqueness of Solutions to the Cauchy Problem for Linear Equations
AbstractThe work proposes a method for analyzing the Cauchy problem for a wide class of linear evolution partial differential equations with variable...
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Discrete Fourier Transform
In the discrete Fourier transform, the Fourier coefficients of a 2π-periodic function, which itself is not given, but whose values are known at...
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Fourier-Transform Method for Partial Differential Equations: Formulas for Representing Solutions to the Cauchy Problem
AbstractThe paper proposes a method for solving the Cauchy problem for linear partial differential equations with variable coefficients of a special...
