28 Aprile, 2017 14:00

Sezione di Geometria, Algebra e loro applicazioni

Reproducing Kernel Hilbert Spaces in the context of Fractional Derivatives

Paula Cerejeiras, Università di Aveiro

Aula Seminari del 3 piano

The idea of a fractional calculus - as already suggested by Leibniz - has seen an increasing interest due to the possibilities for a more accurate description of numerous physical problems either because it provides a new degree of freedom which can be used for more complete characterization of an object or as an additional encoding parameter. In this talk we present a general framework for a function theory based on fractional Cauchy-Riemann operators. Using suitable basic monogenic powers and associated Fueter series we study Gleason's problem and reproducing kernel Hilbert spaces, like the Drury-Arveson space and de Branges-Rovnyak space. We present a counterpart of the Beurling-Lax theorem in the fractional Clifford-Arveson space and give a characterization of the Schur-Agler classes. If time allows we will end with a statement on Schur multipliers in this fractional setting.