Abstract
We discuss determination of jumps for functions with generalized bounded variation. The questions are motivated by A. Gelb and E. Tadmor [1], F. Móricz [5] and [6] and Q. L. Shi and X. L. Shi [7]. Corollary 1 improves the results proved in B. I. Golubov [2] and G. Kvernadze [3].
Similar content being viewed by others
References
A. Gelb and E. Tadmor, Detection of edges in spectral data, Appl. Comput. Harmon. Anal., 7 (1999), 101–135.
B. I. Golubov, Determination of jump of a function of bounded p-variation by its Fourier series, Math. Notes, 12 (1972), 444–449.
G. Kvernadze, Determination of jumps of a bounded function by Its Fourier series, J. Approx. Theory, 92 (1998), 167–190.
F. Lukács, Über die Bestimmung des Sprunges einer Funktion aus ihrer Fourierreihe, J. reine angew. Math., 150 (1920), 107–122.
F. Móricz, Determination of jumps in terms of Abel-Poisson means, Acta Math. Hungar., 98 (2003), 259–262.
F. Móricz, Ferenc Lukács type theorems in terms of the Abel-Poisson mean of conjugate series, Proc. Amer. Math. Soc., 131 (2003), 1234–1250.
Q. L. Shi and X. L. Shi, Determination of jumps in terms of spectral date, Acta Math. Hungar., (2006), to appear.
X. L. Shi, On ΛBMV Functions with some applications to the theory of Fourier series, Sci. Sinica. Ser., A28 (1985), 147–158.
D. Waterman, On covergence of functions of generalized bounded variation, Studia Math., 44 (1972), 107–117.
A. Zygmund, Trigonometric Series, Cambridge University Press (Cambridge, UK, 1959).
Author information
Authors and Affiliations
Additional information
Supported by NSFC 10671062.
Rights and permissions
About this article
Cite this article
Hu, L., Shi, X.L. Concentration factors for functions with harmonic bounded mean variation. Acta Math Hung 116, 89–103 (2007). https://doi.org/10.1007/s10474-007-5298-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-007-5298-0