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We study infinite products of reproducing kernels with view to their use in dynamics (of iterated function systems), in harmonic analysis, and in stochastic processes. On the way, we construct a new family of representations of the Cuntz relations. Then, using these representations we associate a fixed filled Julia set with a Hilbert space. This is based on analysis and conformal geometry of a fixed rational mapping $R$ in one complex variable, and its iterations.
A bounded linear operator $T$ on a Hilbert space is said to be homogeneous if $varphi(T)$ is unitarily equivalent to $T$ for all $varphi$ in the group M{o}b of bi-holomorphic automorphisms of the unit disc. A projective unitary representation $sigma$
The composition operators preserving total non-negativity and total positivity for various classes of kernels are classified, following three themes. Letting a function act by post composition on kernels with arbitrary domains, it is shown that such
We study extensions of Sobolev and BV functions on infinite-dimensional domains. Along with some positive results we present a negative solution of the long-standing problem of existence of Sobolev extensions of functions in Gaussian Sobolev spaces from a convex domain to the whole space.
We investigate connections between the geometry of linear subspaces and the convergence of the alternating projection method for linear projections. The aim of this article is twofold: in the first part, we show that even in Euclidean spaces the conv
This work is devoted to the study of Bessel and Riesz systems of the type $big{L_{gamma}mathsf{f}big}_{gammain Gamma}$ obtained from the action of the left regular representation $L_{gamma}$ of a discrete non abelian group $Gamma$ which is a semidire