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7 - Fourier Series

from Part III - Discrete Functional Analysis

Published online by Cambridge University Press:  06 January 2022

Martin Buntinas
Martin Buntinas
Affiliation:
Loyola University, Chicago
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Summary

Inner Product Spaces and their Fourier Series are studied in this chapter, including Hilbert Spaces and Adjoint Operators. Convergence of Trigonometric and Square Wave Fourier Series of Integrable Functions are investigated. Theorems connecting Summability of Fourier Series and Summability Kernels are studied. The Radamacher, Walsh, and Haar Systems are defined and studied. The Fourier Transform is introduced.

Keywords

Inner Product SpaceFourier SeriesHilbert SpaceSummability KernelsTrigonometric SeriesSquare Wave SeriesRademacher SystemWalsh SystemHaar System, Fourier Transform
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Classical and Discrete Functional Analysis with Measure Theory , pp. 255 - 332
Publisher: Cambridge University Press
Print publication year: 2022

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  • Fourier Series
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.012
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  • Fourier Series
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.012
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Fourier Series
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.012
Available formats
×