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Full-Text Articles in Other Mathematics
On The Reproducing Kernel Hilbert Spaces Associated With The Fractional And Bi-Fractional Brownian Motions, Daniel Alpay, David Levanony
On The Reproducing Kernel Hilbert Spaces Associated With The Fractional And Bi-Fractional Brownian Motions, Daniel Alpay, David Levanony
Mathematics, Physics, and Computer Science Faculty Articles and Research
We present decompositions of various positive kernels as integrals or sums of positive kernels. Within this framework we study the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions. As a tool, we define a new function of two complex variables, which is a natural generalization of the classical Gamma function for the setting we consider.
Rational Functions Associated To The White Noise Space And Related Topics, Daniel Alpay, David Levanony
Rational Functions Associated To The White Noise Space And Related Topics, Daniel Alpay, David Levanony
Mathematics, Physics, and Computer Science Faculty Articles and Research
Motivated by the hyper-holomorphic case we introduce and study rational functions in the setting of Hida’s white noise space. The Fueter polynomials are replaced by a basis computed in terms of the Hermite functions, and the Cauchy-Kovalevskaya product is replaced by the Wick product.
A Characterization Of Schur Multipliers Between Character-Automorphic Hardy Spaces, Daniel Alpay, M. Mboup
A Characterization Of Schur Multipliers Between Character-Automorphic Hardy Spaces, Daniel Alpay, M. Mboup
Mathematics, Physics, and Computer Science Faculty Articles and Research
We give a new characterization of character-automorphic Hardy spaces of order 2 and of their contractive multipliers in terms of de Branges Rovnyak spaces. Keys tools in our arguments are analytic extension and a factorization result for matrix-valued analytic functions due to Leech.