Davit Baramidze disputerer for ph.d.-graden i ingeniørvitenskap / Davit Baramidze will defend his thesis for the PhD degree in Engineering Science.
Davit Baramidze disputerer for ph.d.-graden i ingeniørvitenskap og vil offentlig forsvare avhandlingen / Davit Baramidze will defend his thesis for the PhD degree in Engineering Science:
“A study of boundedness related to some maximal operators of Fejér means on martingale Hardy spaces”.
Avhandlingen er tilgjengelig her (lenke kommer) / The doctoral thesis is available here (link is coming).
Auditoriet er åpent for publikum. Disputasen vil også bli strømmet. Opptak av disputasen vil være tilgjengelig i en måned. / The auditorium is open to the public. The defense will be streamed. A recording of the defense will be available for one month.
Prøveforelesningen starter kl. 10:15 / The trial lecture starts at 10:15. Tittel / title:
“Mathematical Modelling for Engineering Sciences”.
Disputasen starter kl. 12:15 / The defense starts at 12:15.
Prøveforelesning strømmes her, disputas strømmes her. / The trial lecture will be streamed here, and defense will be streamed here.
Sammendrag av avhandlingen / Summary of the thesis:
The classical Fourier Analysis has been developed in an almost unbelievable way from the first fundamental discoveries by Fourier. Especially a number of wonderful results have been proved and new directions of such research has been developed e.g. concerning Wavelets Theory, Gabor Theory, Time-Frequency Analysis, Fast Fourier Transform, Abstract Harmonic Analysis, etc. One important reason for this is that this development is not only important for improving the "State of the art", but also for its importance in other areas of mathematics and also for several applications (e.g. theory of signal transmission, multiplexing, filtering, image enhancement, coding theory, digital signal processing and pattern recognition). The classical theory of Fourier series deals with decomposition of a function into sinusoidal waves. Unlike these continuous waves the Vilenkin (Walsh) functions are rectangular waves. The development of the theory of Vilenkin-Fourier series has been strongly influenced by the classical theory of trigonometric series. Because of this it is inevitable to compare results of Vilenkin series to those on trigonometric series. There are many similarities between these theories, but there exist differences also. Much of these can be explained by modern abstract harmonic analysis, which studies orthonormal systems from the point of view of the structure of a topological group.
The aim of this PhD thesis is to discuss, develop and apply the newest developments of this fascinating theory connected to modern harmonic analysis. In particular, we investigate (Hp − Lp) and weak-(Hp − Lp) type inequalities for maximal operators of Féjer means of Walsh-Fourier series, for 0 < p ≤ 1/2. It is also proved that these results are the best possible in a special sense. As applications both some well-known and new results are pointed out.
Veiledere / Supervisors:
Hovedveileder / Main supervisor:
Professor Lars-Erik Persson, Department of Computer Science and Computational Engineering, Faculty of Engineering Science and Technology, UiT The Arctic University of Norway.
Biveiledere / Co-supervisors:
Bedømmelseskomité / Evaluation committee:
Prøveforelesning og disputas ledes av prodekan for forskning, Svein-Erik Sveen /
The trial lecture and defense are led by Vice Dean of research, Svein-Erik Sveen.
De som ønsker å opponere ex auditorio kan sende e-post til Svein-Erik Sveen / Opponents ex auditorio should contact Svein-Erik Sveen.