Proceedings of the International Conference on Geometry, Integrability and Quantization

Geometric Aspects of Multiple Fourier Series Convergence on the System of Correctly Counted Sets

Viktor Olevskyi and Yuliia Olevska

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

For multiple Fourier series the convergence of partial sums essentially depends on the type of integer sets, to which the sequence numbers of their terms belong. The problem on the general form of such sets is studying in $u$-convergence theory ($u(K)$ - convergence) for multiple Fourier series. An alternative method of summation is based on the concept of the so-called correctly denumarable sets. In the paper some results describing the $u$-convergence relations and convergence on the system or correctly denumarable sets are presented. It is shown that the system of $U(K)$-sets containing a sphere of infinitely increasing radius for fixed $K$ is correctly denumarable. It is established that for the functions satisfying the Lipschitz condition and having a certain growthing $p-k$-variation, the coefficients of multiple Fourier series decrease at the average on the system of $U(K)$-sets faster than it is predicted by their ordinary estimations. It is shown the accurate estimation of the Fourier coefficients of functions of several variables is achieved at a very ``poor'' set of elements of the integer lattice.

Article information

Source
Proceedings of the Nineteenth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2018), 159-167

Dates
First available in Project Euclid: 23 December 2017

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1513998426

Digital Object Identifier
doi:10.7546/giq-19-2018-159-167

Mathematical Reviews number (MathSciNet)
MR3586166

Citation

Olevskyi, Viktor; Olevska, Yuliia. Geometric Aspects of Multiple Fourier Series Convergence on the System of Correctly Counted Sets. Proceedings of the Nineteenth International Conference on Geometry, Integrability and Quantization, 159--167, Avangard Prima, Sofia, Bulgaria, 2018. doi:10.7546/giq-19-2018-159-167. https://projecteuclid.org/euclid.pgiq/1513998426


Export citation