A CantorLebesgue theorem with variable ``coefficients''
Authors:
J. Marshall Ash, Gang Wang and David Weinberg
Journal:
Proc. Amer. Math. Soc. 125 (1997), 219228
MSC (1991):
Primary 42A05; Secondary 42A50, 42A55
MathSciNet review:
1350931
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Abstract 
References 
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Additional Information
Abstract: If is a lacunary sequence of integers, and if for each , and are trigonometric polynomials of degree then must tend to zero for almost every whenever does. We conjecture that a similar result ought to hold even when the sequence has much slower growth. However, there is a sequence of integers and trigonometric polynomials such that tends to zero everywhere, even though the degree of does not exceed for each . The sequence of trigonometric polynomials tends to zero for almost every , although explicit formulas are developed to show that the sequence of corresponding conjugate functions does not. Among trigonometric polynomials of degree with largest Fourier coefficient equal to , the smallest one ``at'' is while the smallest one ``near'' is unknown.
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 R. Cooke, The CantorLebesgue theorem, Amer. Math. Monthly 86(1979), 558565. MR 81b:42019
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 W. Rudin, Real and Complex Analysis, 3rd ed., McGrawHill, New York, 1987. MR 88k:00002
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Additional Information
J. Marshall Ash
Email:
mash@math.depaul.edu
Gang Wang
Affiliation:
(J. M. Ash and G. Wang) Department of Mathematics, DePaul University, Chicago, Illinois 606143504
Email:
gwang@math.depaul.edu
David Weinberg
Affiliation:
(D. Weinberg)Department of Mathematics, Texas Tech University, Lubbock, Texas 794091042
Email:
weinberg@math.ttu.edu
DOI:
http://dx.doi.org/10.1090/S0002993997035685
PII:
S 00029939(97)035685
Keywords:
Cantor Lebesgue theorem,
conjugate trigonometric series,
lacunary trigonometric series,
Plessner's theorem,
trigonometric polynomials
Received by editor(s):
July 27, 1995
Additional Notes:
The research of J. M.\ Ash and G. Wang was partially supported by a grant from the Faculty and Development Program of the College of Liberal Arts and Sciences, DePaul University
Communicated by:
Christopher D. Sogge
Article copyright:
© Copyright 1997
American Mathematical Society
