Keywords
- Orthonormal System
- Orthogonal System
- Maximal Inequality
- Complete Orthonormal System
- Entropy Number
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
I. Agaev, Lacunary subsets of orthonormal sets, Analysis Math. 11 (1985), 283–301.
G. Bennett, L. Dor, V. Goodman, W.B. Johnson, C. Newman, On uncomplemented subspaces of L p, 1 < p < 2, Israel J. Math. 26 (1977), 178–187.
Y. Benjamini, Y. Gordon, Random factorizations of operators between Banach spaces, J. d'Analyse Math. Jerusalem 39 (1981), 45–75.
P. Billard, Sur la convergence presque partout des séries de Fourier-Walsh des fonctions de l'espace L 2[0,1], Studia Math. 28 (1966–67), 363–388.
J. Bourgain, Bounded orthogonal systems and the Λ(p)-set problem, preprint IHES 1988, to appear in Acta Math.
J. Bourgain, J. Lindenstrauss, V. Milman, Approximation of zonoids by zonotopes, Acta Math. (to appear).
L. Carleson, On convergence and growth of partial sums of Fourier series, Acta Math. 116 (1966), 135–157.
C. Fefferman, On the divergence of multiple Fourier series, Bull AMS 77, NO. 2 (1971), 191–195.
T. Figiel, J. Lindenstrauss, V. Milman, Almost spherical sections of convex bodies, Acta Math. 139 (1977), 53–94.
A. Garsia, Existence of almost everywhere convergent rearrangments of Fourier series of L 2-functions, Ann. of Math. 79 (1964), 623–629.
A. Garsia, Topics in almost everywhere convergence, Lectures in Advanced Math, Markham Publ. Co. (Chicago), 1970.
B.S. KĂshin, A.A. Saakyn, Orthogonal systems (Russian), Moscow 1984.
B.S. KĂshin, Trudy Math. Stiklov, 143 (1988), 68–87.
B.S. KĂshin, Properties of random matrices connected with unconditional convergence almost everywhere, Soviet Math. Dolkady 22, N2, (1980), 584–587.
S. Kaczmarz, H. Steinhaus, Theorie der Orthogonalreihen, Warsaw Monografje Matematyczne 1935. Russian translation, Moscow 1958.
A. Kolmogorov, Une contribution à l'étude de convergence des séries de Fourier, Fund. Math. 5 (1924), 96–97.
J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Springer LNM, 1977.
J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II, Springer LNM, 1979.
M. Marcus and G. Pisier, Random Fourier series with Applications to Harmonic Analysis, Annals Math. Studies 101, Princeton UP 1981.
V. Milman and G. Schechtman, Asymptotic theory of normed linear spaces, Springer LNM 1200 (1986).
A.M. Olevskii, Fourier series with respect to general orthogonal systems, Springer Ergebnisse der Math., Band 86 (1975).
H. Rademacher, Einige Sätze über Reihen von allgemeinen Orthogonal-funktionen, Math. Ann. 87 (1922), 112–138.
I. Schur, Über endlich Gruppen und Hermitsche Formen, Math. Zeitschr. 1 (1) (1918), 184–207.
E. Stein, On limits of sequences of operators, Annals Math. 74 (1961), 140–170.
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© 1989 Springer-Verlag
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Bourgain, J. (1989). On kolmogorov's rearrangement problem for orthogonal systems and garsia's conjecture. In: Lindenstrauss, J., Milman, V.D. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1376. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090057
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DOI: https://doi.org/10.1007/BFb0090057
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