Wiener's Approximation Theorem for Locally Compact Abelian Groups

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This study of classical and modern harmonic analysis extends the classical Wiener's approximation theorem to locally compact abelian groups. The first chapter deals with harmonic analysis on the n-dimensional Euclidean space. Included in this chapter are some properties of functions in L1(Rn) and T1(Rn), the Wiener-Levy theorem, and Wiener's approximation theorem. The second chapter introduces the notion of standard function algebra, cospectrum, and Wiener algebra. An abstract form of Wiener's approximation theorem and its generalization is obtained. The third chapter introduces the dual group of a locally compact abelian group, defines the Fourier transform of functions in L1(G), and establishes ... continued below

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iii, 46 leaves

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Shu, Ven-shion August 1974.

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This thesis is part of the collection entitled: UNT Theses and Dissertations and was provided by UNT Libraries to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 44 times , with 4 in the last month . More information about this thesis can be viewed below.

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  • Shu, Ven-shion

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This study of classical and modern harmonic analysis extends the classical Wiener's approximation theorem to locally compact abelian groups. The first chapter deals with harmonic analysis on the n-dimensional Euclidean space. Included in this chapter are some properties of functions in L1(Rn) and T1(Rn), the Wiener-Levy theorem, and Wiener's approximation theorem. The second chapter introduces the notion of standard function algebra, cospectrum, and Wiener algebra. An abstract form of Wiener's approximation theorem and its generalization is obtained. The third chapter introduces the dual group of a locally compact abelian group, defines the Fourier transform of functions in L1(G), and establishes several properties of functions in L1(G) and T1(G). Wiener's approximation theorem and its generalization for L1(G) is established.

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iii, 46 leaves

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  • August 1974

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  • June 24, 2015, 9:39 a.m.

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  • Aug. 25, 2016, 12:12 p.m.

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Shu, Ven-shion. Wiener's Approximation Theorem for Locally Compact Abelian Groups, thesis, August 1974; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc663188/: accessed October 17, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .