Seminar za matematičku analizu i primjene 27.5.2022.

27.5.2022 u 11:00 h u učionici 360 Radmile Matejčić 2, 51000 Rijeka, na Seminaru za matematičku analizu i primjene predavanje će održati Ivana Slamić, Fakultet za matematiku, Sveučilišta u Rijeci. Naslov predavanja je: Maximal Cyclic Subspaces for Dual Integrable Representations.

Maximal principal shift-invariant spaces play an important role in the theory of wavelets. Maximality is characterized by the strict positivity of the periodization function, the property which also appears in characterization of several independence and basis-related properties for the system of integer translates. In this talk, we consider the concept in a more general setting of LCA groups and unitary dual integrable representations. We describe the dual integrable triples which allow a decomposition of the Hilbert space into an orthogonal sum of n maximal cyclic subspaces and analyze how the questions concerning maximality are reflected in redundancy and basis related properties of the generating orbit. Of particular interest is the case when n=1, when the generating orbit is complete in the whole space. The talk is based on a joint work with Hrvoje Šikić.