Convergence of Multiple Fourier Series of Functions of Bounded Generalized Variation
- 50 Downloads
The paper introduces a new concept of Λ-variation of multivariable functions and studies its relationship with the convergence of multidimensional Fourier series.
KeywordsFourier Series Double Fourier Series Trigonometric Fourier Series Harmonic Variation Multiple Fourier Series
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Unable to display preview. Download preview PDF.
- 2.Z. A. Chanturia, “The modulus of variation of a function and its application in the theory of Fourier series,” Sov. Math. Dokl., 15, 67–71 (1974).Google Scholar
- 4.M. I. Dyachenko, “Two-dimensional Waterman classes and u-convergence of Fourier series,” Mat. Sb., 190, No. 7, 23–40 (1999); English translation: Sb. Math., 190, No. 7-8, 955–972 (1999).Google Scholar
- 10.G. H. Hardy, “On double Fourier series and especially which represent the double zeta function with real and incommensurable parameters,” Quart. J. Math. Oxford Ser., 37, 53–79 (1906).Google Scholar
- 13.A. I. Sablin, “Λ-variation and Fourier series,” Izv. Vysch. Uchebn. Zaved., Mat., 10, 66–68 (1987); English translation: Sov. Math. Izv. Vuzov, 31 (1987).Google Scholar
- 14.A. A. Sahakian, “On the convergence of double Fourier series of functions of bounded harmonic variation,” Izv. Akad. Nauk Arm. SSR. Ser. Mat., 21, No. 6, 517–529 (1986); English translation: Sov. J. Contemp. Math. Anal., 21, No. 6, 1–13 (1986).Google Scholar
- 16.D. Waterman, “On the summability of Fourier series of functions of Λ-bounded variation,” Stud. Math., 54, No. 1, 87–95 (1975/76).Google Scholar
© Springer Science+Business Media New York 2015