Szegő’s theorem on a bidisc
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- by Takahiko Nakazi PDF
- Trans. Amer. Math. Soc. 328 (1991), 421-432 Request permission
Abstract:
G. Szegö showed that \[ \inf \;\int _0^{2\pi } {|1 - f{|^2}w d\theta /2\pi = \exp \;\int _0^{2\pi } {\log w d\theta /2\pi } } \] where $f$ ranges over analytic polynomials with mean value zeros. We study extensions of the Szegö’s theorem on the disc to the bidisc. We show that the quantity is a mixed form of an arithmetic mean and a geometric one of $w$ in some special cases.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 328 (1991), 421-432
- MSC: Primary 32A35; Secondary 32A37, 46J15
- DOI: https://doi.org/10.1090/S0002-9947-1991-1028762-2
- MathSciNet review: 1028762