Giorgi Tutberidze disputerer for ph.d.-graden i ingeniørvitenskap og vil offentlig forsvare avhandlingen / Giorgi Tutberidze will defend his thesis for the PhD degree in Engineering Science:
“A study of bounded operators on martingale Hardy spaces”
Disputasen vil bli strømmet. Opptak av disputasen vil være tilgjengelig i en måned.
The defense will be streamed. A recording of the disputation will be available for one month.
Prøveforelesningen starter kl. 10:15 / The trial lecture starts at 10:15. Tittel / title:
“Mathematics in engineering applications”
Disputasen starter kl. 12:15 / The defense starts at 12:15.
De som ønsker å opponere ex auditorio kan sende e-post til leder av disputasen, professor Raymond Kristiansen.
Opponents ex auditorio should sign up to leader of defense by e-mail to professor Raymond Kristiansen.
Sammendrag av avhandlingen / Summary of the thesis:
The aim of my thesis is to discuss, develop and apply the newest developments of this fascinating theory connected to modern harmonic analysis. In particular, we investigate some strong convergence result of partial sums of Vilenkin-Fourier series. Moreover, we derive necessary and sufficient conditions for the modulus of continuity so that norm convergence of subsequences of Fejér means is valid. Furthermore, we consider Riesz and Nörlund logarithmic means. 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. In addition, we investigate some T means, which are "inverse" summability methods of Nörlund, but only in the case when their coefficients are monotone.
According to the problems, methods of real analysis combined with methods of abstract and non-linear harmonic analysis together with theory of approximation will be widely used. Other research methods include theory of function theory.
Veiledere / Supervisors:
Hovedveileder / Main supervisor:
Dr. George Tephnadze, The University of Georgia.
Medveiledere / Co-supervisors:
Professor Lars-Erik Persson, Department of Computer Science and Computational Engineering, UiT The Arctic University of Norway.
Professor Dag Lukkassen, Department of Computer Science and Computational Engineering, UiT The Arctic University of Norway.
Bedømmelseskomité / Evaluation committee:
Associate Professor Károly Nagy, Institute of Mathematics and Informatics, Eszteházy Károly University (1st opponent)
Professor Nacima Memić, Department of mathematics, University of Sarajevo (2nd opponent)
Professor Arne Lakså, Department of Computer Science and Computational Engineering, UiT The Arctic University of Norway (administrator of the committee)
Prøveforelesning og disputas ledes av prodekan, professor Raymond Kristiansen / The trial lecture and defense is led by Vice Dean, Professor Raymond Kristiansen.