Moment problems, biorthogonals and applications to control theory


From January 19th, 2018 to January 30th, 2018
Fridays and Tuesdays, 11:30-13:00. Please check Dates and rooms.

Prof. Sorin Micu

University of Craiova (Craiova, România)

Abstract:
The problem of moments received its first systematic treatment in the late 19th and early 20th centuries through the works of P. L. Chebyshev, A. A. Markov, T. Stieltjes, H. Hamburger, P. Nevannlina, M. Riesz, T. Carleman and many others. In spite of its quite old origin, it continues to exert profound influence on the development of analysis and its applications to a wide variety of fields. In particular, the theory of systems and control is no exception. The aim of this course is to introduce the main concepts and techniques related to the non-Fourier moment problem for the exact and approximate controllability of infinite dimensional systems.

Contents:

  1. Introduction: Fourier transform, Entire functions of exponential type, Paley-Wiener Theorem, distribution of zeros of entire functions of exponential type;
  2. Families of exponential functions: completeness, minimality, uniform minimality, biortogonals;
  3. Applications to the control of hyperbolic problems: Wave, Schrödinger, Benjamin Bona Mahony equations;
  4. Application to the control of parabolic problems: heat equation and anomalous diffusion equations;
  5. A general method for constructing biortogonals to families of exponential functions.


Dates and rooms (Today is )

DATE PRESENTER ROOM
Friday, January 19th 2018 Sorin Micu TIMON Room at DeustoTech
Tuesday, January 23rd 2018 Sorin Micu TIMON Room at DeustoTech
Friday, January 26th 2018 Sorin Micu TIMON Room at DeustoTech
Tuesday, January 30th 2018 Sorin Micu TIMON Room at DeustoTech