Nenad Teofanov: föredragsserie
Välkommen till en föredragsserie i seminarieserien i matematik.
Föreläsare/Lecturer
Nenad Teofanov, professor, University of Novi Sad, Serbien
Välkommen till enskilda föredrag eller till hela serien.
Föredrag 1, måndag 2 mars kl 14.15-15.00 i sal K2054, hus K
Regularity and decay: spaces of type S
We recall the definition and main properties of Gelfand-Shilov spaces. Elements of such spaces satisfy prescribed decay and regularity conditions which makes them useful in different situations. We briefly discuss topology and main operators acting on those spaces. We also recall beautiful symmetric characterizations in the spirit of Chung, Chung and Kim (1996). The lecture ends with a comment on non-triviality of Gelfand-Shilov spaces.
Föredrag 2, tisdag 3 mars kl 16.15-17.00 i sal B1006, hus B
Gelfand-Shilov spaces and Hermite expansions
Fourier transform invariant Gelfand-Shilov spaces enjoy additional convenient characterizations. We begin with Hermite functions and related expansions. This gives a characterization of functions from Gelfand-Shilov spaces by decay properties of the sequence of coefficients in related expansions. We give a detailed proof which enlightens the main techniques used in the study of Gelfand-Shilov spaces.
Föredrag 3, onsdag 4 mars kl 13.15-14.00 i sal D1172, hus D
Gelfand-Shilov spaces and powers of harmonic oscillator
The role of the Hermite operator (the Schrodinger harmonic oscillator operator) in characterization of is Gelfand-Shilov spaces is revealed. More precisely, we will show that such can be described by the means of iterates of Hermite operator. Several remarks will be given, also related to a recent result of Toft et al. (2020) in the context of Pilipovic spaces.
Föredrag 4, torsdag 5 mars kl 15.15-16.00 i sal B1006, hus B
Time-frequency representations and Gelfand-Shilov spaces
We recall results of Grochenig and Zimmermann (2004) and their extension by Toft (2012, 2017) who gave characterization of Gelfand-Shilov spaces by the means of the short-time Fourier transform. A detailed exposition of the proof is given, and followed by an alternative proof that follows from theorems given in previous lectures.