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Mathematical Analysis Fundamentals by Agamirza Bashirov

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Chapter 12

Fourier Series and Integrals

Abstract

Chapter 12 presents Fourier series. Pointwise, uniform and mean square convergence of Fourier series and conditions for them are discussed. Fourier series in abstract inner product spaces is also considered. Cesàro summability and Fejér’s theorem are presented. Completeness of trigonometric functions, Gibb’s phenomenon are discussed. The chapter ends with introduction to Fourier integrals.

Keywords

Fourier series; orthogonal functions; Cesaro summability; Gibb’s phenomenon; Fourier integral

Fourier99 series and integrals form an area in mathematics that clearly demonstrates that the language of nature is mathematical. Having purely abstract mathematical content, Fourier series and integrals are widely ...

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