Stationary frames and spectral estimation. (English) Zbl 0763.42017
Probabilistic and stochastic methods in analysis, with applications, Proc. NATO Adv. Study Inst., Il Ciocco/Italy 1991, NATO ASI Ser., Ser. C 372, 117-161 (1992).
[For the entire collection see Zbl 0746.00060.]
The paper contains a discussion of recent results in connection with the problems posed by A. N. Kolmogorov in Bull. Moscov. Gosudarst. Univ., Math. 2, No. 6, 1-40 (1941) and related to A: Prediction theory, B: Spectral theory of minimal stationary sequences, C: Wiener-Khinchin theorem.
After a short Introduction (Section 1) the author gives a commentary on some parts of Kolmogorov’s paper (Section 2). Section 3 is devoted to weighted norm inequalities for Fourier transform which are intimately connected with the Prediction theory (item A). Section 4 is related to item B and devoted to stationary frames. In Section 5 the author states his recent results related to the spherical Wiener-Plancherel formula.
The paper contains a discussion of recent results in connection with the problems posed by A. N. Kolmogorov in Bull. Moscov. Gosudarst. Univ., Math. 2, No. 6, 1-40 (1941) and related to A: Prediction theory, B: Spectral theory of minimal stationary sequences, C: Wiener-Khinchin theorem.
After a short Introduction (Section 1) the author gives a commentary on some parts of Kolmogorov’s paper (Section 2). Section 3 is devoted to weighted norm inequalities for Fourier transform which are intimately connected with the Prediction theory (item A). Section 4 is related to item B and devoted to stationary frames. In Section 5 the author states his recent results related to the spherical Wiener-Plancherel formula.
Reviewer: B.Rubin (Jerusalem)
