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Topics in Classical and Modern Analysis pp 315–330Cite as

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Fixed Volume Discrepancy in the Periodic Case

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Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

The smooth fixed volume discrepancy in the periodic case is studied here. It is proved that the Frolov point sets adjusted to the periodic case have optimal in a certain sense order of decay of the smooth periodic discrepancy. The upper bounds for the r-smooth fixed volume periodic discrepancy for these sets are established.

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Acknowledgements

The author would like to thank the Erwin Schrödinger International Institute for Mathematics and Physics (ESI) at the University of Vienna for support. This paper was started when the author participated in the ESI-Semester “Tractability of High Dimensional Problems and Discrepancy,” September 11–October 13, 2017. The work was supported by the Russian Federation Government Grant No. 14.W03.31.0031.

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Authors and Affiliations

  1. University of South Carolina, Columbia, SC, USA

    Vladimir N. Temlyakov

  2. Steklov Institute of Mathematics, Moscow, Russia

    Vladimir N. Temlyakov

  3. Lomonosov Moscow State University, Moscow, Russia

    Vladimir N. Temlyakov

Authors
  1. Vladimir N. Temlyakov
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Editor information

Editors and Affiliations

  1. Georgia Southern University, Statesboro, GA, USA

    Martha Abell

  2. Georgia Southern University, Statesboro, GA, USA

    Emil Iacob

  3. Georgia Southern University, Statesboro, GA, USA

    Alex Stokolos

  4. Georgia Southern University, Statesboro, GA, USA

    Sharon Taylor

  5. ICREA, Passeig de Lluís Companys, Barcelona, Spain ; Centre de Recerca Matemàtica, Barcelona, Spain

    Sergey Tikhonov

  6. Georgia Southern University, Statesboro, GA, USA

    Jiehua Zhu

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Temlyakov, V.N. (2019). Fixed Volume Discrepancy in the Periodic Case. In: Abell, M., Iacob, E., Stokolos, A., Taylor, S., Tikhonov, S., Zhu, J. (eds) Topics in Classical and Modern Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-12277-5_20

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