Prediction $n$ units of time ahead
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- by Takahiko Nakazi and Katutoshi Takahashi PDF
- Proc. Amer. Math. Soc. 80 (1980), 658-659 Request permission
Abstract:
The purpose of this note is to give a simple expression in terms of w of the quantities \[ {\rho _n}(w) = \inf \limits _f \int _0^{2\pi } {|1 + {e^{in\theta }}f{|^2}w d\theta /2\pi } \quad (n = 0,1,2, \ldots ),\] where f ranges over the analytic trigonometric polynomials with mean value zero and w is nonnegative and summable on the circle.References
- Ulf Grenander and Gabor Szegö, Toeplitz forms and their applications, California Monographs in Mathematical Sciences, University of California Press, Berkeley-Los Angeles, 1958. MR 0094840
- Henry Helson, Lectures on invariant subspaces, Academic Press, New York-London, 1964. MR 0171178
- Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008
- T. L. Kriete III, On the Fourier coefficients of outer functions, Indiana Univ. Math. J. 20 (1970/71), 147–155. MR 412429, DOI 10.1512/iumj.1970.20.20014
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 658-659
- MSC: Primary 60G25; Secondary 30D55
- DOI: https://doi.org/10.1090/S0002-9939-1980-0587949-1
- MathSciNet review: 587949