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Basic Analysis I, 2020
Publisher Summary This chapter analyzes trigonometric Fourier series, which are series of trigonometric functions. This set is chosen because the mathematics is the best developed and is the simplest to demonstrate. It will serve to illustrate the basic questions that need to be addressed for each system.
James K. Peterson
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Publisher Summary This chapter analyzes trigonometric Fourier series, which are series of trigonometric functions. This set is chosen because the mathematics is the best developed and is the simplest to demonstrate. It will serve to illustrate the basic questions that need to be addressed for each system.
James K. Peterson
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Introduction to Fourier series
Hermitian Analysis, 2019From the other side, in 1876 P. du Bois-Reymond found a continuous function whose Fourier series diverges at a single point. Via the uniform boundedness theorem, we will show later that there are continuous functions whose Fourier series diverges at any ...
Charles L. Epstein
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Essentials of Mathematical Methods in Science and Engineering, 2019
The extension of the Fourier calculus to the entire real line leads naturally to the Fourier transform, a powerful mathematical tool for the analysis of aperiodic functions.
Massoud Malek
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The extension of the Fourier calculus to the entire real line leads naturally to the Fourier transform, a powerful mathematical tool for the analysis of aperiodic functions.
Massoud Malek
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Combined Estimator Fourier Series and Spline Truncated in Multivariable Nonparametric Regression
, 2015Multivariable additive nonparametric regression model is a nonparametric regression model that involves more than one predictor and has additively separable function on each predictor. There are many functions that can be used on nonparametric regression
I. W. Sudiarsa+3 more
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Fourier Series and Fourier Transforms
2003In Chapter 3, we touched upon the analogy between the diffraction of x-rays and that of visible light. Here, we extend that discussion and consider some aspects of Fourier series and Fourier transforms.
Mark Ladd, Rex A. Palmer
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On the Fourier series and Fourier transforms
Journal of Mathematical Sciences, 2019This survey article is addresses to classical harmonic analysis. In particular, a number of classical theorems are presented with the simplest, in our opinion, proofs (see also [1] and references therein). Some results of the present article are new and are published for the first time.
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Use of Fourier series in the analysis of discontinuous periodic structures
, 1996The recent reformulation of the coupled-wave method by Lalanne and Morris [ J. Opt. Soc. Am. A13, 779 ( 1996)] and by Granet and Guizal [ J. Opt. Soc. Am. A13, 1019 ( 1996)], which dramatically improves the convergence of the method for metallic gratings
Lifeng Li
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Strong Convergence of Two-Dimensional Walsh–Fourier Series
Ukrainian Mathematical Journal, 2013We prove that certain means of quadratic partial sums of the two-dimensional Walsh–Fourier series are uniformly bounded operators acting from the Hardy space Hp to the space Lp for 0
G. Tephnadze
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1966
Publisher Summary This chapter focuses on “function space” as opposed to a three-dimensional “vector space.” This function space is infinite dimensional, in the sense that an infinite sequence of mutually orthogonal functions is needed to represent an arbitrary function.
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Publisher Summary This chapter focuses on “function space” as opposed to a three-dimensional “vector space.” This function space is infinite dimensional, in the sense that an infinite sequence of mutually orthogonal functions is needed to represent an arbitrary function.
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Simulating Spatial Averages of Stationary Random Field Using the Fourier Series Method
, 2013A Fourier series method (FSM) of simulating spatial averages of stationary Gaussian random fields is presented. The FSM is able to simulate spatial averages over nonequally spaced rectangular cells, and by adopting Gauss quadrature, it can be further ...
S. Jha, J. Ching
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