Affiliation:
1. South West University “Neofit Rilski” , Blagoevgrad , Bulgaria
Abstract
Abstract
In the present paper the author uses the function system Γ
ℬ
s
constructed in Cantor bases to show upper bounds of the extreme and star discrepancy of an arbitrary net in the terms of the trigonometric sum of this net with respect to the functions of this system. The obtained estimations are inequalities of the type of Erdős-Turán-Koksma. These inequalities are very suitable for studying of nets constructed in the same Cantor system.
Reference13 articles.
1. [1] CHRESTENSON, H. E.: A class of generalized Walsh functions, Pacific J. Math. 5 (1955), 17–31.10.2140/pjm.1955.5.17
2. [2] DRMOTA, M.—TICHY, R. F.: Sequences, Discrepancies and Applications. In: Lecture Notes in Math. Vol. 1651, Springer-Verlag, Berlin, 1997.
3. [3] ERDŐS, P.—TURÁN, P.: On a problem in the theory of uniform distribution, I, II. Indag. Math. 10 (1948), 370–378; 406–413.
4. [4] GROZDANOV, V.—PETROVA, TS.: The function system Γℬs and its applications to the theory of Quasi-Monte Carlo integration and uniformly distributed sequen (to appear).
5. [5] HELLEKALEK, P.: General discrepancy estimates: the Walsh function system, Acta Arith. 67 (1994), 209–218.10.4064/aa-67-3-209-218