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Continued Fractions, Wavelet Time Operators and Inverse Problems

2003
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Rocky Mountain Journal of Mathematics
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The spectral properties of the analytic theory of continued fractions, orthogonal functions, and rational approximation, are examined from the point of view of operator theory. New historical and mathematical perspectives are provided. Then a general question is posed: what spectral information is needed to uniquely determine an operator? The time operator induced by an arbitrary wavelet basis is presented as an example. This question is then directed at continued fractions. 1. Introduction.

doi:10.1216/rmjm/1181069972
fatcat:radoh3ef3fcyhb6l3erut2v2ka