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A Constructive Proof of Beurling-Lax Theorem 被引量：1

A Constructive Proof of Beurling-Lax Theorem
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摘要 This paper deals with an alternative proof of Beurling-Lax theorem by adopting a constructive approach instead of the isomorphism technique which was used in the original proof. This paper deals with an alternative proof of Beurling-Lax theorem by adopting a constructive approach instead of the isomorphism technique which was used in the original proof.
作者 Qiuhui CHEN Tao QIAN
机构地区 Cisco School of Informatics Department of Mathematics
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2015年第1期141-146,共6页 数学年刊（B辑英文版）
基金 supported by the Multi-Year Research Grant(No.MYRG115(Y1-L4)-FST13-QT) the Multi-Year Research Grant(No.MYRG116(Y1-L3)-FST13-QT) Macao Government(No.FDCT098/2012/A3) the Natural Science Foundation of Guangdong Province(No.S2011010004986)
关键词 构造性证明 定理 同构 Beurling-Lax theorem,Shift operator,Inner function
分类号 O177 [理学—基础数学]
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参考文献10

  • 1Aleksandrov, A. B., Embedding theorem for coinvariant subspaces of the shift operator, Zap. Nauchn. Sere. S. -Peterburg, Otel. Math. Inst. Steklov, 262, 1999, 5-48.
  • 2Beurling, A., On two problems concerning linear transformations in Hilbert space, Acta Math., 81, 1949, 239-255.
  • 3Cima, J. and Ross, W., The Backward Shift on the Hardy Space, American Mathematical Society, Provi- dence, RI, 2000.
  • 4Douglas, R. G., Shapiro, H. S. and Shields, A. L., Cyclic vectors and invariant subspace for the backward shift invariant subspace, Annales de l'Institut Fourier, 20, 1970, 37-76.
  • 5Hoffman, K., Banach Spaces of Analytic Functions, Prentice-Hall, Englewood Cliffs, New Jersey, 1962.
  • 6Jaming, P., Phase retrieval techniques for radar ambiguity problems, Journal of Fourier Analysis and Applications, 5, 1999, 309 329.
  • 7Lax, P. D., Translation invariant spaces, Acta Mathematic, 101, 1959, 163-178.
  • 8Qian, T., Chen, Q. and Tan, L., The rational orthogonal systems are Schauder bases, Complex Variable and Elliptic Equations, DOI: 10.1080/17476933.2013.787532, 2013.
  • 9Stein, E. M. and Weiss, G., Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, New Jersey, 1975.
  • 10Tan, L. and Qian, T., Backward shift invariant subspace of band-limited signals and generalizations of Titehmarsh's theorem, manuscript, 2012.

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Chinese Annals of Mathematics,Series B
2015年 第1期

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