Piecewise linear spectral sequences

Authors:
Youming Liu and Yuesheng Xu

Journal:
Proc. Amer. Math. Soc. **133** (2005), 2297-2308

MSC (2000):
Primary 42C15

DOI:
https://doi.org/10.1090/S0002-9939-05-08067-6

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 and introduce the concept of spectral sequences. We characterize piecewise linear spectral sequences with the knot at 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:
https://doi.org/10.1090/S0002-9939-05-08067-6

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