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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Piecewise linear spectral sequences


Authors: Youming Liu and Yuesheng Xu
Journal: Proc. Amer. Math. Soc. 133 (2005), 2297-2308
MSC (2000): Primary 42C15
Published electronically: March 21, 2005
MathSciNet review: 2138872
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Abstract | References | Similar Articles | Additional Information

Abstract: We study a class of orthonormal exponential bases for the space $L^2[0,1]$ and introduce the concept of spectral sequences. We characterize piecewise linear spectral sequences with the knot at $1/2$ and investigate the non-continuity of the piecewise linear spectral sequences. From a special construction of a piecewise constant spectral sequence, the classical Walsh system is recovered.


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Additional Information

Youming Liu
Affiliation: Department of Applied Mathematics, Beijing Polytechnic University, Pingle Yuan 100, Beijing 100022, People’s Republic of China

Yuesheng Xu
Affiliation: Department of Mathematics, 215 Carnegie Hall, Syracuse University, Syracuse, New York 13244 – and – Institute of Mathematics, Academy of Mathematics and System Sciences, The Chinese Academy of Sciences, Beijing 100080, People’s Republic of China

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08067-6
PII: S 0002-9939(05)08067-6
Keywords: Orthonormal exponential bases, non-constant frequency, spectral sequences, Walsh systems
Received by editor(s): September 11, 2003
Published electronically: March 21, 2005
Additional Notes: The first author was supported in part by the Natural Science Foundation of Beijing, No. 1022002
The second author was supported in part by the US National Science Foundation under grants 9973427 and 0312113, by the Natural Science Foundation of China under grant 10371122 and by the Chinese Academy of Sciences under the program “One Hundred Distinguished Chinese Young Scientists”
Communicated by: David R. Larson
Article copyright: © Copyright 2005 American Mathematical Society