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Strong converse inequality for Poisson sums

Author(s): F. Dai; Z. Ditzian
Journal: Proc. Amer. Math. Soc. 133 (2005), 2609-2611.
MSC (2000): Primary 41A17, 41A63
Posted: April 25, 2005
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Abstract | References | Similar articles | Additional information

Abstract: The rate of convergence of Poisson sums and their combinations are shown to be equivalent to appropriate $K$-functionals.

References:

[Ch-Di]
W. Chen and Z. Ditzian, Best approximation and $K\text{-functionals}$, Acta Math. Hungar. 75 (1997), 165-208. MR 1440498 (98h:41013)

[Da]
F. Dai, Some equivalence theorems with $K\text{-functionals}$, Jour. of Approx. Theory 121 (2003), 143-157. MR 1963000 (2003m:42013)

[Di]
Z. Ditzian, Fractional derivatives and best approximation, Acta Math. Hungar. 81 (4) (1998), 323-348. MR 1662219 (2000e:41046)

[Di-Iv]
Z. Ditzian and K. Ivanov, Strong converse inequalities, Jour. d'Analyse Math. 61 (1993), 61-111. MR 1253439 (94m:41038)

[Ha]
G.H. Hardy, Divergent Series, Oxford Univ. Press, 1948. MR 0030620 (11:25a)

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Additional Information:

F. Dai
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

Z. Ditzian
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

DOI: 10.1090/S0002-9939-05-08089-5
PII: S 0002-9939(05)08089-5
Received by editor(s): January 27, 2004
Posted: April 25, 2005
Additional Notes: This work was supported by NSERC grant of Canada A4816
Communicated by: Andreas Seeger
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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