@article{MASLO_1994_44_5_a11,
author = {Strauch, Oto},
title = {$L\sp 2$ discrepancy},
journal = {Mathematica slovaca},
pages = {601--632},
year = {1994},
volume = {44},
number = {5},
mrnumber = {1338433},
zbl = {0818.11029},
language = {en},
url = {http://geodesic.mathdoc.fr/item/MASLO_1994_44_5_a11/}
}
Strauch, Oto. $L\sp 2$ discrepancy. Mathematica slovaca, Tome 44 (1994) no. 5, pp. 601-632. http://geodesic.mathdoc.fr/item/MASLO_1994_44_5_a11/
[1] JACOBS K.: Measure and Integral. Academic Press, New York-San Francisco-London, 1978. | MR | Zbl
[2] KUIPERS L.-NIEDERREITER H.: Uniform Distribution of Sequences. John Wiley & Sons, New York, 1974. | MR | Zbl
[3] KUIPERS L.: Remark on the Weyl-Schoenberg criterion in the theory of asymptotic distribution of real numbers. Nieuw Arch. Wisk. (3) 16 (1968), 197-202. | MR | Zbl
[4] LEVEQUE W. J.: An inequality connected with Weyľs criterion for uniform distribution. In: Theory of Numbers. Proc. Sympos. Pure Math., Calif. Inst. Tech., Pasadena, Calif. 1963. Vol. VIII, Amer. Math. Soc, Providence, R. I., 1965, pp. 22-30. | MR
[5] DE MATHAN B.: Approximations diophantiennes dans un corps local. Bull. Soc. Math. France, Mémoire 21 (1970). | MR | Zbl
[6] SCHOENBERG I. J.: Über die asymptotische Verteilung reeller Zahlen mod 1. Math. Z. 28 (1928), 171-199. | MR
[7] STRAUCH O.: On the $L^2$ discrepancy of distances of points from a finite sequence. Math. Slovaca 40 (1990), 245-259. | MR
[8] STRAUCH O.: A new moment problem of distribution functions in the unit interval. Math. Slovaca 44 (1994), 171-211. | MR | Zbl
[9] STRAUCH O.: Duffìn-Schaeffer conjecture and some new types of real sequences. Acta Matli. Univ. Comenian. XL-XLI (1982), 233-265. | MR | Zbl
[10] WINKLER R.: Some remarks on pseudorandom sequences. Math. Slovaca 43 (1993), 493-512. | MR | Zbl
[11] ZINTERHOF P.: Über einige Abschätzungen bei der Approximation von Funktionen mit Gleгchverteilungsmethoden. Sitzungsber. Österreich. Akad. Wiss. Math.-Natur. Kl II 185 (1976), 121-132. | MR
[12] GOLDSTERN M.: The complexity of uniform distribution. Math. Slovaca 44 (1994), 491-500. | MR | Zbl
[13] DOBROVOLSKII N. M.: An effective proof of Roth's theorem on quadratic deviation. (Russian), Uspekhi Mat. Nauk 39 (1984), 155-156. | MR
[14] WEYL H.: Über die Gleгchverteгlung von Zahlen mod. Eins. Math. Ann. 77 (1916), 313-352. | MR
[15] VAN DER CORPUT J. G.-PISOT C.: Sur la discrépance modulo un. Indag. Math. 1 (1939), 143-153, 184-195, 260-269. | Zbl
[16] FAST H. : Sur la convergence statistique. Colloq. Math. 2 (1951), 241-244. | MR | Zbl
[17] SCHOENBERG I. J.: The integrability of certain functions and related summability methods. Amer. Math. Monthly 66 (1959), 361-375. | MR | Zbl
[18] NIEDERREITER H.: Application of diophantine approximations to numerical integration. In: Diophantine Approximation and Its Applications (C F. Osgood, ed.), Academic Press, New York, 1973, pp. 129-199. | MR | Zbl
[19] KOKSMA J. F.: Een algemeene stelling uit de theorie der gelijmatige verdeeling modulo 1. Mathematica B (Zutphen) 11 (1942/43), 7-11. | MR
[20] GRABNER P. J., ICHY R. F.: Remarks on statistical independence of sequences. Math. Slovaca 44 (1994), 91-94. | MR
[21] GEL'FAND I. M., JAGLOM A. M.: Integration in functional spaces and its application in quantum physics. (Russian), Uspekhi Mat. Nauk 11 (1956), 77-114. | MR
[22] SHOHAT J. A., TAMARKIN J. D.: The Problem of Moments. Mathematical Surveys, Amer. Math. Soc., Providence, Rhode Island, 1943. | MR | Zbl