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Fourier Series
Chapter 1 covers the classical theory of Fourier series of...
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Fourier Restriction Implies Maximal and Variational Fourier Restriction in Lorentz Space
In this paper, we show that Fourier restriction theorem implies the maximal and variational Fourier restriction in Lorentz space frame. The key...
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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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Real Paley-Wiener Theorems for the Space-Time Fourier Transform
This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to...
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Discrete Fourier Transforms
This chapter deals with the discrete Fourier transform (DFT). In Sect. 3.1, we show that numerical realizations of Fourier methods, such as the...
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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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Fourier coefficients of Hilbert modular forms at cusps
The aim of this article is to study the fields generated by the Fourier coefficients of Hilbert newforms at arbitrary cusps. Precisely, given a...
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Fourier Modes in Fluid Flow and Energy Cascade
The main challenge for wind engineers nowadays is the precise prediction of peak wind pressures on buildings, which are determined by the surrounding...
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Uniform maximal Fourier restriction for convex curves
We extend the estimates for maximal Fourier restriction operators proved by Müller et al. (Rev Mat Iberoam 35:693–702, 2019) and Ramos (Proc Am Math...
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Quantum signal processing and nonlinear Fourier analysis
Elucidating a connection with nonlinear Fourier analysis (NLFA), we extend a well known algorithm in quantum signal processing (QSP) to represent...
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Application of the extended Fourier amplitude sensitivity testing (FAST) method to inflated, axial stretched, and residually stressed cylinders
This paper is dedicated to applying the Fourier amplitude sensitivity test (FAST) method to the problem of mixed extension and inflation of a...
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Fourier Series
The chapter is an introduction to the theory of Fourier series. We present here some aspects of Fourier series as applicable to practical problems in...
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Rate of Convergence for Double Rational Fourier Series
We calculate the rate of convergence of the double rational Fourier series for regular, bounded, measurable, and two-variable functions. The...
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The Fourier transform and multipliers
In this chapter, we complement the discussion of three major themes of Fourier analysis that we have studied in the previous Volumes.
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Fourier Methods
This endows its integral with special properties in terms of Fourier transforms, making Fourier theory intimately related to the geophysical...
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The Fourier spectrum and sumset type problems
We introduce and study the Fourier spectrum which is a continuously parametrised family of dimensions living between the Fourier dimension and the...
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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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Fourier Series
In Chap. 4 we discuss the expansion of periodic functions into infinite trigonometric series (introduced by Joseph Fourier in the early 1800s)....