ODT - THESIS TOPIC: György Gát: Investigation of convergence properties ...


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Thesis topic proposal

Investigation of convergence properties of Fourier series with respect to locally constant orthonormal systems

THESIS TOPIC PROPOSAL

Institute: University of Debrecen
mathematics and computing
Doctoral School of Mathematical and Computational Sciences

Thesis supervisor: György Gát
Location of studies (in Hungarian): University of Debrecen
Abbreviation of location of studies: UD IM

Description of the research topic:

A Walsh function maps from [0,1] and can only take 1 or -1 as a value. The sequence of the Walsh functions forms a complete orthonormal system. The main aim of the research is to investigate the convergence and divergence properties of the Walsh-Fourier series of one and multidimensional functions. Also to investigate of various summation methods with respect to Walsh and Walsh-like systems. Especially, norm convergence and divergence with respect to various norms. It is recommended to have a look at paper
http://www.emis.de/journals/AMAPN/vol14/GAT.PDF
or to have a look at the book Schipp, F.; Wade, W. R.; Simon, P., Walsh Series. An Introduction to Dyadic Harmonic Analysis. Budapest, Akadémiai Kiadó 1990. X, 560 pp.

Number of students who can be accepted: 1

Deadline for application: 2018-02-16

2024. IV. 17.
ODT ülés
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