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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Unconditional basic sequence in $L^p(\mu )$ and its $l^p$-stability
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by Lihua Yang PDF
Proc. Amer. Math. Soc. 127 (1999), 455-464 Request permission

Abstract:

This paper is concerned with unconditional basic sequences in $L^p(\mu )$. We prove that, under some conditions, a sequence in $L^p(\mu )$ is a bounded unconditional basic sequence if and only if it is $l^p$-stable. At last the results are applied to the shift-invariant basic sequences generated by a finite subset of $L^p(R^s)$, which is very important in wavelet analysis.
References
    Guerre, S. Classical Sequences in Banach Spaces, Marcel Dekker, 1992.
  • Rong Qing Jia and Charles A. Micchelli, Using the refinement equations for the construction of pre-wavelets. II. Powers of two, Curves and surfaces (Chamonix-Mont-Blanc, 1990) Academic Press, Boston, MA, 1991, pp. 209–246. MR 1123739
  • Jia, R.Q., Refinable Shift-invariant Spaces: From Spline to Wavelets Approximation Theory VIII, Vol.2: Wavelets and Multilevel Approximation, Charles K. Chui and Larray L. Schumaker (eds.), (179–208) 1995.
  • Yves Meyer, Wavelets and operators, Cambridge Studies in Advanced Mathematics, vol. 37, Cambridge University Press, Cambridge, 1992. Translated from the 1990 French original by D. H. Salinger. MR 1228209
  • Ingrid Daubechies, Ten lectures on wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 61, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992. MR 1162107, DOI 10.1137/1.9781611970104
  • Kôsaku Yosida, Functional analysis, 2nd ed., Die Grundlehren der mathematischen Wissenschaften, Band 123, Springer-Verlag New York, Inc., New York, 1968. MR 0239384
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Additional Information
  • Lihua Yang
  • Affiliation: Department of Scientific Computing and Computer Applications, Zhongshan University, 510275, People’s Republic of China; Institute of Mathematics, Academy Sinica, Beijing, 100080, People’s Republic of China
  • Email: yang@comp.hkbu.edu.hk, ylh@math03.math.ac.cn
  • Received by editor(s): October 14, 1996
  • Received by editor(s) in revised form: May 21, 1997
  • Communicated by: J. Marshall Ash
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 455-464
  • MSC (1991): Primary 46B20
  • DOI: https://doi.org/10.1090/S0002-9939-99-04638-9
  • MathSciNet review: 1473673