We introduce and study the Split Common Null Point Problem (SCNPP) for set-valued maximal monotone mappings in Hilbert space. This problem generalizes our Split Variational Inequality Problem (SVIP) [Y. Censor, A. Gibali and S. Reich, Algorithms for the split variational inequality problem, Numerical Algorithms, accepted for publication, DOI 10.1007/s11075-011-9490-5]. The SCNPP with only two s...

A classical theorem of C. Fefferman [3] says that the characteristic function of the unit disc is not a Fourier multiplier on L(R) unless p = 2. In this article we obtain a result that brings a contrast with the previous theorem. We show that the characteristic function of the unit disc in R is the Fourier multiplier of a bounded bilinear operator from L1(R) × L2(R) into L(R), when 2 ≤ p1, p2 <...

Let f : X→ R be a convex mapping and X a Hilbert space. In this paper we prove the following refinement of Jensen’s inequality: E(f |X ∈ A) ≥ E(f |X ∈ B ) for every A,B such that E(X |X ∈ A) = E(X |X ∈ B ) and B ⊂ A. Expectations of Hilbert space valued random elements are defined by means of the Pettis integrals. Our result generalizes a result of Karlin and Novikov (1963), who derived it for ...

versity A state process is described by either a discrete time Hilbert space valued process, or a stochastic differential equation in Hilbert space. The state is observed through a finite dimensional process. Using a change of measure and a Fusive theorem the Zakai equation is obtained in discrete or continuous time. A risk sensitive state estimate is also defined.

An extension of the auxiliary problem principle to variational inequalities with non-symmetric multi-valued operators in Hilbert spaces is studied. This extension concerns the case that the operator is splitted into the sum of a single-valued operator F , possessing a kind of pseudo Dunn property, and a maximal monotone operator Q. The current auxiliary problem is constructed by fixing F at the...

this paper introduces an implicit scheme for a   continuous representation of nonexpansive mappings on a closed convex subset of a hilbert space with respect to a   sequence of invariant means defined on an appropriate space of bounded, continuous real valued functions of the semigroup.   the main result is to    prove the strong convergence of the proposed implicit scheme to the unique solutio...

We propose a general matrix-valued multiple kernel learning framework for highdimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to be imposed on a dictionary of vector-valued Reproducing Kernel Hilbert Spaces. We develop a highly scalable and eigendecompositionfree algorithm that orchestr...

We propose a general matrix-valued multiple kernel learning framework for highdimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to be imposed on a dictionary of vector-valued Reproducing Kernel Hilbert Spaces [19]. We develop a highly scalable and eigendecomposition-free Block coordinate ...

This paper presents a framework for computing random operator-valued feature maps for operator-valued positive definite kernels. This is a generalization of the random Fourier features for scalar-valued kernels to the operator-valued case. Our general setting is that of operator-valued kernels corresponding to RKHS of functions with values in a Hilbert space. We show that in general, for a give...

The basic mathematical framework for super Hilbert spaces over a Graßmann algebra with a Graßmann number-valued inner product is formulated. Super Hilbert spaces over infinitely generated Graßmann algebras arise in the functional Schrödinger representation of spinor quantum field theory in a natural way. a email: [email protected]