Notes regarding classical Fourier series
Keywords:convergence, infinite series, uniform, bounded, periodic, trigonometric, Fourier
A survey of some classical results from the theory of trigonomtrical series is presented, especially the case of Fourier series. Some new proofs are presented, and Riemann's theory of trigonometrical series is is given special attention.
R.E Edwards, Fourier Series, a modern introduction, 2nd ed, Springer-Verlag, NY, 1979. DOI: https://doi.org/10.1007/978-1-4612-6208-4_8
W. Rudin, Principles of Mathematical Analysis, McGraw Hill, 3rd ed, NY, 1976.
W. Cheney, Analysis for Applied Mathematics, Springer-Verlag, NY, 2001. DOI: https://doi.org/10.1007/978-1-4757-3559-8
E. Hewitt, K. Stromberg, Real and Abstract Analysis, Springer-Verlag, NY, 1965. DOI: https://doi.org/10.1007/978-3-642-88047-6
E.T. Whitaker, G.N. Watson, A Course of Modern Analysis, Cambridge University Press, 4th ed, Cambridge, 1973.
E.C. Titchmarsh, Eigenfunction expansions associated with second-order differential operators, Oxford, Clarendon Press, 1946.
D. Bleecker, G. Csorles, Basic Partial Differential Equations, International Press, Cambridge, 1995.
H. Weyl, Ramifications, Old and New, of the Eigenvalue Problem, Bull. of the AMS, 56, 1950, pp.~115--139. DOI: https://doi.org/10.1090/S0002-9904-1950-09369-0
S. Bochner, Summation of classical Fourier series: An application to Fourier expansions on compact Lie groups, Ann. of Math. 17, (1936), pp.~345--356. DOI: https://doi.org/10.2307/1968447
O. Vejvoda, Partial differential equations: time-periodic solutions, M Nijhoff Publishers, The Hague, 1982. DOI: https://doi.org/10.1007/978-94-009-7672-6
J.W. Brown, R.V. Churchill, Fourier Series and Boundary Value Problems, 7th ed, McGraw Hill, Boston, 2008.
How to Cite
Copyright (c) 2023 Paul Bracken
This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.