We prove a new criterion that guarantees self-adjointness of Toeplitz operators with unbounded operator-valued symbols. Our applies, in particular, to symbols Lipschitz continuous derivatives, which is the natural class Hamiltonian functions for classical mechanics. For this we extend Berger-Coburn estimate case vector-valued Segal-Bargmann spaces. Finally, apply our result (operator-valued) qu...

This article deals with vector valued diierential forms on C 1-manifolds. As a generalization of the exterior product, we introduce an operator that combines Hom(N s (W); Z)-valued forms with Hom(N s (V); W)-valued forms. We discuss the main properties of this operator such as (multi)linearity, associa-tivity and its behavior under pullbacks, push-outs, exterior diierentiation of forms, etc. Fi...

In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...

We establish a generalized Jensen’s inequality for analytic vector-valued functions on TN using a monotonicity property of vector-valued Hardy martingales. We then discuss how this result extends to functions on a compact abelian group G, which are analytic with respect to an order on the dual group. We also give a generalization of Helson and Lowdenslager’s version of Jensen’s inequality to ce...

In this paper we consider a class of distributed parameter systems (partial differential equations) determined by strongly nonlinear operator valued measures in the setting of the Gelfand triple V ↪→ H ↪→ V ∗ with continuous and dense embeddings where H is a separable Hilbert space and V is a reflexive Banach space with dual V ∗. The system is given by dx+A(dt, x) = f(t, x)γ(dt) +B(t)u(dt), x(0...

Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the celebrated Random Fourier Feature methodology to get an approximation of operatorvalued kernels. We propose a general principle for Operator-valued Random Four...

We consider the problem of learning a vector-valued function f in an online learning setting. The function f is assumed to lie in a reproducing Hilbert space of operator-valued kernels. We describe two online algorithms for learning f while taking into account the output structure. A first contribution is an algorithm, ONORMA, that extends the standard kernel-based online learning algorithm NOR...