<abstract xmlns="http://www.w3.org/1999/xhtml"> Let γq(n) be the van der Corput sequence in the base q and g(x, y, z, u) be an asymptotic distribution function of the 4-dimensional sequence<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/Untitled-8.jpg"></inline-graphic></alternatives></inline-formula>In this paper we find an explicit formula for g(x, x, x, x) and then as an example we find the limit<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/Untitled-9.jpg"></inline-graphic></alternatives></inline-formula>for the base q = 4, 5, 6, . . . Also we find an explicit form of sth iteration T(s)(x) of the von Neumann-Kakutani transformation defined by T(γq(n)) = γq(n + 1). </abstract>

Let γq(n) be the van der Corput sequence in the base q and g(x, y, z, u) be an asymptotic distribution function of the 4-dimensional sequenceIn this paper we find an explicit formula for g(x, x, x, x) and then as an example we find the limitfor the base q = 4, 5, 6, . . . Also we find an explicit form of sth iteration T(s)(x) of the von Neumann-Kakutani transformation defined by T(γq(n)) = γq(n + 1).

The asymptotic distribution function of the 4-dimensional shifted van der corput sequence

Slovak Technical University Radlinského 12 SK–812-37 Bratislava SLOVAKIA

Trnava University in Trnava Priemyselná 4 SK–918-43 Trnava SLOVAKIA

Graz University of Technology Steyrergasse 30 AT–8010 Graz AUSTRIA

University of Calabria Via P. Bucci 30B I–87036 Arcavacata di Rende (CS) ITALY

Mathematical Institute Slovak Academy of Sciences Štefánikova 49 SK–814-73 Bratislava SLOVAKIA

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Let γq(n) be the van der Corput sequence in the base q and g(x, y, z, u) be an asymptotic distribution function of the 4-dimensional sequenceIn this paper we...

The asymptotic distribution function of the 4-dimensional shifted van der corput sequence

Publié en ligne: 19 févr. 2016

Pages: 75 - 92

Reçu: 27 oct. 2015

DOI: https://doi.org/10.1515/tmmp-2015-0043

Mots clés
uniform distribution, distribution function

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The asymptotic distribution function of the 4-dimensional shifted van der corput sequence

Publié en ligne: 19 févr. 2016

Pages: 75 - 92

Reçu: 27 oct. 2015

DOI: https://doi.org/10.1515/tmmp-2015-0043

Mots clésuniform distribution, distribution function

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
uniform distribution, distribution function