Λ(𝑞) processes

Blei, Ron C.

doi:10.1090/S0002-9947-1990-0974517-3

$\Lambda (q)$ processes
HTML articles powered by AMS MathViewer

by Ron C. Blei

Trans. Amer. Math. Soc. 319 (1990), 777-786

DOI: https://doi.org/10.1090/S0002-9947-1990-0974517-3

PDF | Request permission

Abstract:

Motivated by some classical notions in harmonic analysis, $\Lambda (q)$ processes are introduced in the context of a study of stochastic interdependencies. An extension of a classical theorem of Salem and Zygmund regarding random Fourier series is obtained. The Littlewood exponent of $\Lambda (q)$ processes is estimated and, in some archetypical cases, computed.

References

Ron C. Blei, Multi-linear measure theory and multiple stochastic integration, Probab. Theory Related Fields 81 (1989), no. 4, 569–584. MR 995812, DOI 10.1007/BF00367304
Ron Blei, Combinatorial dimension and certain norms in harmonic analysis, Amer. J. Math. 106 (1984), no. 4, 847–887. MR 749259, DOI 10.2307/2374326
Ron C. Blei, $\alpha$-chaos, J. Funct. Anal. 81 (1988), no. 2, 279–297. MR 971881, DOI 10.1016/0022-1236(88)90101-2
Ron C. Blei and J.-P. Kahane, A computation of the Littlewood exponent of stochastic processes, Math. Proc. Cambridge Philos. Soc. 103 (1988), no. 2, 367–370. MR 923689, DOI 10.1017/S030500410006494X
Ron C. Blei, Measurements of interdependencies of stochastic increments, Commutative harmonic analysis (Canton, NY, 1987) Contemp. Math., vol. 91, Amer. Math. Soc., Providence, RI, 1989, pp. 29–36. MR 1002585, DOI 10.1090/conm/091/1002585
J. Bourgain, Bounded orthogonal systems and the $\Lambda (p)$-set problem, Acta Math. 162 (1989), no. 3-4, 227–245. MR 989397, DOI 10.1007/BF02392838
Yitzhak Katznelson, An introduction to harmonic analysis, Second corrected edition, Dover Publications, Inc., New York, 1976. MR 0422992

On bounded bilinear forms in an infinite number of variables

1

H. P. McKean, Geometry of differential space, Ann. Probability 1 (1973), 197–206. MR 353471, DOI 10.1214/aop/1176996973
Walter Rudin, Trigonometric series with gaps, J. Math. Mech. 9 (1960), 203–227. MR 0116177, DOI 10.1512/iumj.1960.9.59013
R. Salem and A. Zygmund, Some properties of trigonometric series whose terms have random signs, Acta Math. 91 (1954), 245–301. MR 65679, DOI 10.1007/BF02393433
Norbert Wiener, The Homogeneous Chaos, Amer. J. Math. 60 (1938), no. 4, 897–936. MR 1507356, DOI 10.2307/2371268