Abstract
Recently several papers (see e.g. [2], [3, [5], [7, [10]) deal with problems of imbedding of classes of functions connected with strong approximation of Fourier series. At such problems the main question is to find conditions implying that a certain class of functions should be imbedded into another one, and one of the classes in question is determined by certain properties of the strong approximation of Fourier series.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alexits, G. — Králik, D., Über den Annährungsgrad der Approximation im starken Sinne von stetigen Funktionen. Magyar Tud. Akad. Mat. Kutató Int. Közl. 8 (1963), 317–327.
Krotov, V.G., Strong approximation by Fourier series and differentiability properties of functions. Analysis Math. 4 (1978), 199–214.
Krotov, V.G. — Leindler, L., On the strong summability of Fourier series and the classes Hω. Acta Sci. Math. (Szeged) 40 (1978), 93–98.
Leindler, L., Über die Approximation im starken Sinne. Acta Math. Acad. Sci. Hungar. 16 (1965), 255–262.
Leindler, L., Strong approximation and classes of functions. Mitt. Math. Sem. Giessen 132 (1978), 29–38.
Leindler, L., Strong and best approximation of Fourier series and the Lipschitz classes. Analysis Math. 4 (1978), 101–116.
Leindler, L., Imbedding theorems and strong approximation. Acta Sci. Math. (Szeged) (to appear).
Leindler, L., Generalizations of Prössdorf’s theorems. Studia Sci. Math. Hungar. (to appear).
Lorentz, G.G., Approximation of functions. Holt, Rinehart and Winston, New York/Chicago/Toronto, 1966.
Totik, V., On structural properties of functions arising from strong approximation of Fourier series. Acta Sci. Math. (Szeged) 41 (1979), 227–251.
Zygmund, A., Trigonometric Series. Cambridge, 1968.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1981 Birkhäuser Verlag Basel
About this chapter
Cite this chapter
Leindler, L. (1981). Strong Approximation and Generalized Lipschitz Classes. In: Butzer, P.L., Sz.-Nagy, B., Görlich, E. (eds) Functional Analysis and Approximation. ISNM 60: International Series of Numerical Mathematics / ISNM 60: Internationale Schriftenreihe zur Numerischen Mathematik / ISNM 60: Série internationale d’Analyse numérique, vol 60. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9369-5_31
Download citation
DOI: https://doi.org/10.1007/978-3-0348-9369-5_31
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9371-8
Online ISBN: 978-3-0348-9369-5
eBook Packages: Springer Book Archive