Fourier分析导论--第1章--Fourier分析的起源(E.M. Stein & R. Shakarchi) Fourier分析导论--第2章--Fourier级数的基本属性(E.M. Stein & R. Shakarchi) Fourier分析导论--第3章--Fourier级数的收敛性(E.M. Stein & R. Shakarchi) Fourier分析导论--第4章--Fourier级数的一些应用(E.M. Stein & R. ...
D'Alembert和其他数学家也有怀疑。Fourier(1807年)在他对热传导方程的研究中改变了这种观点,他的执着信念和卓越的工作最终导致了其他数学家完全证明了一般函数都可以表示成Fourier级数。 内容来源: <<Fourier Analysis: An Introduction>> E.M. Stein & R. Shakarchi ...
Butzer, P., Nessel, R.: Fourier Analysis and Approximation. Academic Press, New York (1971) Book Google Scholar Stein, E., Weiss, G.: Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press, Princeton (1971) MATH Google Scholar Stein, E., Shakarchi, R.: Fourier...
SolutionstosomeexercisesandproblemsfromSteinandShakarchi’sFourierAnalysisThebookbyYKetznelson,”AnintroductionofHar-monicAnalysis”(2ndcorrectededition)isreferredtofrequentlyChapter1:TheGenesisofFourierAnalysis Chapter2:BasicPropertiesofFourierSeries Chapter3:ConvergenceofFourierSeries ...
in R? (Stein & Shakarchi 2003). In quantum mechanics, the momentum and position wave functions are Fourier transform pairs, to within a factor of Planck's constant. With this constant properly taken into account, the inequality above becomes the statement of the Heisenberg uncertainty principle ...
But here it uses the analog for the Fourier transform (Corollary 2.6 in Chapter 2 in stein's Functional Analysis [2]): Theorem 6.4.1. If 1\leq p\leq 2 and \frac{1}{p}+\frac{1}{q}=1, then the Fourier transform T has a unique extension to a bounded map from L^p to L^q,...
Stein and Shakarchi move from an introduction addressing "Fourier" series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory. Fourier ...