Dissertation: Generalized Schur functions and passive discrete-time realizations

In his dissertation, Lassi Lilleberg examines generalized Shur functions and passive discrete-time realizations in Pontryagin space setting. The dissertation lies in the field of operator theory. The research also applies the methods originated from mathematical systems theory and complex analysis.

 The study develops and combines the standard theory of passive discrete-time systems and ordinary Schur functions with the characteristic function realization theory of generalized Schur functions, says Lilleberg, who will defend his doctoral dissertation at the University of Vaasa on Friday 9th of April.

Defect functions were defined and used for the first time for generalized Schur functions.

– This provides tools to analyze other indefinite function spaces. The results have also applications in the mathematical system theory.

The research topic interested Lilleberg because it was not so far from topics that he had already studied during his master's degree. Some researchers of the University of Vaasa had also strong backgrounds from the field.

Mathematics is logical, exact and eternal

Lilleberg, who lives in Laihia, Finland, says that the doctoral studies in mathematics were a natural choice for him.

– My master’s studies were interesting, satisfying and my grades were excellent. It was natural to pursue towards doctoral studies and dissertation.

– I am interested in the logic, exactness and eternity of mathematics; results will not get out of date, even though new results will be published all the time.

Lilleberg reveals that the ease of mathematical research is also fascinating.

– I do not need large amounts of data like measurements, interviews or statistics. I can solve my research problems pretty much the same way as everybody else has solved their mathematical exercises in the school, Lilleberg tells.

Public defence

The public examination of M.Sc. Lassi Lilleberg’s doctoral dissertation "Generalized Schur functions and passive discrete-time realizations" will be held on Friday 9 April 2021 at noon.

The event will be organised online: https://uwasa.zoom.us/j/67661419012?pwd=M25UMGZON2RvcnY3UEwrM2E3K1Y4UT09
Password: 405677

Dr. Michael Dritschel (Newcastle University ) will act as an opponent and Professor Seppo Hassi as custos.

Lilleberg, Lassi (2021) Generalized Schur functions and passive discrete-time realizations. Acta Wasaensia 425. Doctoral dissertation. Vaasan yliopisto / University of Vaasa.

Publication pdf: http://urn.fi/URN:ISBN:978-952-476-943-3

Further information

Lassi Lilleberg, tel +358 40 322 9919, lassi.lilleberg (@) uwasa.fi

Mathematics and statistics
Technology and Innovations