Skip to main content

Fourier Series

  • Chapter
  • First Online:
  • 1589 Accesses

Abstract

Fourier series decompose periodic functions or periodic signals into the sum of a countable family of simple oscillating functions, namely sines and cosines (or complex exponentials).

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Carleson, L.: On the convergence and growth of partial sums of Fourier series. Acta Math. 116, 135–157 (1966)

    Google Scholar 

  2. Bhatia, R.: Notes on Functional Analysis. Hindustan Book Agency, New Delhi (2009)

    MATH  Google Scholar 

  3. Vladimirov, V.S.: Equations of Mathematical Physics. Marcel Dekker, New York (1971)

    Google Scholar 

  4. Gonzalez-Velasco, E.A.: Connections in mathematical analysis: the case of Fourier series. Am. Math. Mon. 99(5), 427–441 (1992)

    Google Scholar 

  5. Zygmund, A.: Trigonometric Series, 2nd edn. Cambridge University Press, Cambridge (1988)

    MATH  Google Scholar 

  6. Boas, R.P.: Summation formulas and band-limited signals. Tohoku Math. J. 24, 121–125 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  7. Steiner, A.: Plancherel’s theorem and the Shannon series derived simultaneously. Am. Math. Mon. 87, 193–197 (1980)

    Article  MATH  Google Scholar 

  8. Higgins, J.R.: Five short stories about the cardinal series. Bull. Am. Math. Soc. 12, 45–89 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  9. Bhatia, R.: Fourier Series. The Mathematical Association of America, Washington (2005)

    Google Scholar 

  10. Grafakos, L.: Classical Fourier Analysis, 2nd edn. Springer, New York (2008)

    MATH  Google Scholar 

  11. Grafakos, L.: Modern Fourier Analysis, 2nd edn. Springer, New York (2009)

    Book  MATH  Google Scholar 

  12. Kaiser, G.: A Friendly Guide to Wavelets. Birkhäuser, Boston (1994)

    MATH  Google Scholar 

  13. Chernoff, P.R.: Pointwise convergence of Fourier series. Am. Math. Mon. 87, 399–400 (1980)

    Google Scholar 

  14. Jordan, C.: Sur la série de Fourier. C.R. Acad. Sci. Paris, 92, 228–230 (1881)

    Google Scholar 

  15. Lebesgue, H.: Leçons sur les séries trigonométriques. Gauthier-Villars, Paris (1906)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. D. R. Choudary .

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer India

About this chapter

Cite this chapter

Choudary, A.D.R., Niculescu, C.P. (2014). Fourier Series. In: Real Analysis on Intervals. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2148-7_12

Download citation

Publish with us

Policies and ethics