Helson, Henry; Lowdenslager, David Prediction theory and Fourier series in several variables. (English) Zbl 0082.28201 Acta Math. 99, 165-202 (1958). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 6 ReviewsCited in 170 Documents Keywords:approximation and series expansion × Cite Format Result Cite Review PDF Full Text: DOI References: [1] N. I. Achieser,Vorlesungen über Approximationstheorie. Berlin. 1953. · Zbl 0052.29002 [2] R. Arens, A Banach algebra generalization of conformal mappings of the disc.Trans. Amer. Math. Soc. 81 (1956), 501–513. · Zbl 0073.33103 · doi:10.1090/S0002-9947-1956-0078658-7 [3] R. Arens &I. M. Singer, Function values as boundary integrals.Proc. Amer. Math. Soc. 5 (1954), 735–745. · Zbl 0056.33501 · doi:10.1090/S0002-9939-1954-0065024-7 [4] R. Arens &I. M. Singer, Generalized analytic functions.Trans. Amer. Math. Soc. 81 (1956), 379–393. · Zbl 0078.10902 · doi:10.1090/S0002-9947-1956-0078657-5 [5] A. Beurling, On two problems concerning linear transformations in Hilbert space.Acta Math. 81 (1949), 239–255. · Zbl 0033.37701 · doi:10.1007/BF02395019 [6] S. Bochner, Boundary values of analytic functions in several variables and of almost periodic functions.Ann. of Math. 45 (1944), 708–722. · Zbl 0060.24302 · doi:10.2307/1969298 [7] A. P. Calderón &A. Zygmund, Singular integrals and periodic functions.Studia Math. 14 (1954), 249–271. · Zbl 0064.10401 [8] J. L. Doob,Stochastic Processes. New York, 1953. [9] B. Fuglede &R. V. Kadison, Determinant theory in finite factors.Ann. of Math. 55 (1952), 520–530. · Zbl 0046.33604 · doi:10.2307/1969645 [10] G. H. Hardy &J. E. Littlewood, Some new properties of Fourier constants.Math. Ann. 97 (1927), 159–209. · JFM 52.0267.01 · doi:10.1007/BF01447865 [11] A. N. Kolmogoroff, Stationary sequences in Hilbert’s space (Russian).Bolletin Moskovskogo Gosudarstvennogo Universiteta. Matematika 2 (1941). (Reference from Mathematical Reviews.) [12] L. H. Loomis,Abstract harmonic analysis. New York, 1953. · Zbl 0052.11701 [13] G. Mackey, The Laplace transform for locally compact Abelian groups.Proc. Nat. Acad. Sci. 34 (1948), 156–162. · Zbl 0030.39803 · doi:10.1073/pnas.34.4.156 [14] N. Wiener &P. Masani, The prediction theory of multivariate stochastic processes. I. The regularity condition.Acta Math., 98 (1957), 111–150. II. The linear predictor.Acta Math., 99 (1958), 93–137. · Zbl 0080.13002 · doi:10.1007/BF02404472 [15] F. & M. Riesz, Über die Randwerte einer analytischen Funktion.Quatrième Congrès des math. scandinaves, 1916, 27–44. [16] G. Szegö, Beiträge zur Theorie der toeplitzschen Formen (Erste Mitteilung).Math. Z. 6 (1920), 167–202. · JFM 47.0391.04 · doi:10.1007/BF01199955 [17] G. Szegö, Über die Randwerte einer analytischen Funktion.Math. Ann. 84 (1921), 232–244. · JFM 48.0332.03 · doi:10.1007/BF01459407 [18] N. Wiener,Extrapolation, interpolation, and smoothing of stationary time series. New York, 1949. · Zbl 0036.09705 [19] N. Wiener, On the factorization of matrices.Comment. Math. Helv. 29 (1955), 97–111. · Zbl 0064.06301 · doi:10.1007/BF02564273 [20] A. Zygmund,Trigonometrical series. Warsaw, 1935. · Zbl 0011.01703 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.