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On a generalization of Smirnov’s theorem with some applications

  • Lasha Ephremidze EMAIL logo and Ilya Spitkovsky
Published/Copyright: March 29, 2018
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Abstract

We present a certain generalization of Smirnov’s theorem on functions from the Hardy spaces Hp. We provide some applications of the proposed generalization. Namely, we give an equivalent characterization of outer analytic rectangular matrix functions, and give a simple proof of the uniqueness of spectral factorization of rank deficient matrices.

MSC 2010: 30J99

References

[1] P. L. Duren, Theory of Hp Spaces, Pure Appl. Math. 38, Academic Press, New York, 1970. Search in Google Scholar

[2] H. Helson and D. Lowdenslager, Prediction theory and Fourier series in several variables. II, Acta Math. 106 (1961), 175–213. 10.1007/BF02545786Search in Google Scholar

[3] P. Koosis, Introduction to Hp Spaces, London Math. Soc. Lecture Note Ser. 40, Cambridge University Press, Cambridge, 1980. Search in Google Scholar

[4] N. K. Nikolski, Operators, Functions, and Systems: An Easy Reading. Vol. 1. Hardy, Hankel, and Toeplitz, Math. Surveys Monogr. 92, American Mathematical Society, Providence, 2002. Search in Google Scholar

Received: 2017-8-1
Accepted: 2018-1-12
Published Online: 2018-3-29
Published in Print: 2018-6-1

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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