Fourier series of functions with infinite discontinuities

Authors

  • Branko Sarić Faculty of Sciences, Trg Dositeja Obradovića 2, 1000 Novi Sad, Serbia; College of Technical Engineering, Professional Studies, Svetog Save 65, 32000 Čačak

DOI:

https://doi.org/10.5644/SJM.10.1.13

Keywords:

total H$_{1}$- integrability, Fourier series

Abstract

Using the total H$_{1}$-integrability concept we shall show that functions, which take on infinite values in the interval $\left( -\pi ,\pi \right)$ at only finitely many places, can be expanded into a \textit{Fourier} series over this interval.

Downloads

Download data is not yet available.

References

R. G. Bartle, A Modern Theory of Integration, Graduate Studies in Math., Vol. 32, AMS, Providence, 2001.

I. J. L. Garces and P. Y. Lee, Convergence theorems for the H$_{1}$-integral, Taiwanese J. Math., 4 (3) (2000), 439-445.

R. A. Gordon, The Integrals of Lebesgue, Denjoy, Perron and Henstock, Graduate Studies in Math., Vol. 4, AMS, Providence, 1994.

J. Marcinkiewicz and A. Zygmund, Two theorems on trigonometrical series, Rec. Math., [Mat. Sbornik] N.S., 2 (44) 4, (1937), 733--737.

E. J. McShane, Partial orderings and Moore-Smith limits, Am. Math. Mon., 59 (1952), 1--11.

B. Sarić, The Fourier series of one class of functions with discontinuities, Doctoral dissertation defended on 20th of October 2009 at the University of Novi Sad, Faculty of Science, Department of Mathematics and Informathics.

B. Sarić, Cauchy's residue theorem for a class of real valued functions, Czech. Math. J., 60 (4) (2010), 1043--1048.

B. Sarić, On totalization of the Henstock – Kurzweil integral in the multidimensional space, Czech. Math. J., 61, (4) (2011), 1017--1022.

B. Sarić, On totalization of the H$_{1}$-integral, Taiw. J. Math., {15} (4) (2011), 1691--1700.

V. Sinha and I. K. Rana, On the continuity of associated interval functions, Real Anal. Exch., 29 (2) (2003/2004), 979--981.

A. Zygmund, Trigonometric series, University Press, Cambridge, 2003.

Downloads

Published

04.06.2024

How to Cite

Sarić, B. (2024). Fourier series of functions with infinite discontinuities. Sarajevo Journal of Mathematics, 10(1), 103–110. https://doi.org/10.5644/SJM.10.1.13

Issue

Section

Articles