Onefold and Twofold Ellis–Gohberg Inverse Problems for Scalar Wiener Class Functions
The theory of onefold and twofold Ellis-Gohberg inverse problems for Wiener functions on the real line is specified further for the scalar case. Assuming the left onefold problem or the right onefold problem to be solvable, a necessary and sufficient condition is given for the twofold problem to be solvable. In that case the left and the right onefold problem are both solvable, and the solutions are equal. An example shows that the latter is not always true, i.e., the left and the right onefold problem are solvable does not imply that the solutions are equal.
KeywordsInverse problem for orthogonal functions Wiener algebra Toeplitz operator Hankel operator Rational functions Inner-outer factorization Realization
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