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Saturation on locally compact abelian groups

  • Walter R. Bloom (a1) and Joseph F. Sussich (a1)

Abstract

Let G be a locally compact abeian group, (μρ) a net of bounded Radon measures on G. In this paper we consider conditions under which (μρ) is saturated in Lp (G) and apply these results to the Fejér and Picard approximation processes.

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References

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[1]Berg, Christian and Forst, Gunnar, Potential theory on locally compact abelian groups (Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 87, Springer-Verlag, Berlin, Heidelberg, New York, 1975).
[2]Buchwalter, Henri, ‘Saturation sur un groupe abélien localement compact’, C. R. Acad. Sci. Paris 250 (1960), 808810.
[3]Butzer, Paul L. and Nessel, Rolf J., Fourier analysis and approximation, Volume 1, One-dimensional theory (Birkhäuser, Basel, Stuttgart, 1971).
[4]DeVore, Ronald A., The approximation of continuous functions by positive linear operators (Lecture Notes in Mathematics, 293, Springer-Verlag, Berlin, Heidelberg, New York, 1972).
[5]Dreseler, Bernd and Schempp, Walter, ‘Saturation on locally compact abelian groups’, Manuscripta Math. 7 (1972), 141174.
[6]Dreseler, Bernd and Schempp, Walter, ‘Approximation on double coset spaces’ in Approximation Theory (Papers, VIth Semester, Stefan Banach Intemat. Math. Center, Warsaw, 1975), pp. 6981, Banach Center Publ., 4, PWN, Warsaw, 1979.
[7]Hewitt, Edwin and Ross, Kenneth A., Abstract harmonic analysis, Volumes I, II (Die Grundlehren der Mathematischen Wissenschaften, Bände 115, 152. Academic Press, New York; Springer-Verlag, Berlin, Göttingen, Heidelberg, 1963, 1970.)
[8]Nishishiraho, Toshihiko, ‘Saturation of positive linear operators’, Töhoku Math. J. 28 (1976), 239243.
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Saturation on locally compact abelian groups

  • Walter R. Bloom (a1) and Joseph F. Sussich (a1)

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