A general notion of lifting properties for families of sesquilinear forms is formulated. These lifting properties, which appear as particular cases in many classical interpolation problems, are studied for the Toeplitz kernels in Z, and applied for refining and extending the Nehari theorem and the Paley lacunary inequality.
Classical Bargmann’s representation is given by operators acting on the space of holomorphic functions with scalar product . We consider the problem of representing the functional F as a measure. We prove the existence of such a measure for q > 1 and investigate some of its properties like uniqueness and radiality.
The Pompeiu and the Morera problems have been studied in many contexts and generality. For example in different spaces, with different groups, locally, without an invariant measure, etc. The variations obtained exhibit the fascination of these problems.In this paper we present a new aspect: we study the case in which the functions have values over a Clifford Algebra. We show that in this context it is completely natural to consider the Morera problem and its variations. Specifically, we show the...
We characterize the existence of the solutions of the truncated moments problem in several real variables on unbounded supports by the existence of the maximum of certain concave Lagrangian functions. A natural regularity assumption on the support is required.
We give several characterizations of the symmetrized n-disc Gₙ which generalize to the case n ≥ 3 the characterizations of the symmetrized bidisc that were used in order to solve the two-point spectral Nevanlinna-Pick problem in ℳ ₂(ℂ). Using these characterizations of the symmetrized n-disc, which give necessary and sufficient conditions for an element to belong to Gₙ, we obtain necessary conditions of interpolation for the general spectral Nevanlinna-Pick problem. They also allow us to give a...