Continued Fractions Associated with Trigonometric and Other Strong Moment Problems
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چکیده
General T-fractions and M-fractions whose approximants form diagonals in two-point Pad6 tables are subsumed here under the study of Perron-Carath6odory continued fractions (PC-fractions) whose approximants form diagonals in weak two-point Pad6 tables. The correspondence of PCfractions with pairs of formal power series is characterized in terms of Toeplitz determinants. For the subclass of positive PC-fractions, it is shown that even ordered approximants converge to Carath6odory functions. This result is used to establish sufficient conditions for the existence of a solution to the trigonometric moment problem and to provide a new starting point for the study of Szeg6 polynomials orthogonal on the unit circle. Szeg6 polynomials are shown to be the odd ordered denominators of positive PC-fractions. Positive PCfractions are also related to Wiener filters used in digital signal processing [3], [251.
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تاریخ انتشار 2005