20170909Reproducing Kernel Hilbert Spaces and Gleason's problem in fractional Clifford analysis
摘要:Fractional calculus - as already suggested by Leibniz - has seen an increasing interest since it allows for a more accurate description of numerous physical problems by providing new degrees of freedom which can be used for a more complete characterization of a given object or additional encoding parameters. 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 the Gleason’s problem and establish reproducing kernel Hilbert spaces, like the Drury-Arveson space and de Branges-Rovnyak space. This allows for a counterpart of the Beurling-Lax theorem in the fractional Clifford-Arveson space. Moreover, a characterization of Schur-Agler classes is given.
20170909Paula Cerejeiras Reproducing Kernel Hilbert Spaces and Gleason's problem in fractional Clifford analysis