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Continuity of solutions to the autocorrelation equation

✍ Scribed by Elias Wegert; Lothar v. Wolfersdorf

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
176 KB
Volume
28
Category
Article
ISSN
0170-4214

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✦ Synopsis

Using Fourier techniques and the inner-outer factorization of holomorphic functions a complete description of the various solutions to the autocorrelation equation on a ΓΏnite interval is given.

The Fourier transform of the solutions admits an representation involving Cauchy integrals and Blaschke products. Using this representation a general e cient criterion for the continuity of the solutions is obtained.

Further, an explicit formula for the values of the (canonical) solution at the endpoints of the interval is derived.

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