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The Newman-Shapiro Isometry Theorem is proved in the case of Segal-Bargmann spaces of entire vector-valued functions (i.e. summable with respect to the Gaussian measure on ℂⁿ). The theorem is applied to find the adjoint of an unbounded Toeplitz operator with φ being an operator-valued exponential polynomial.
Let f be an analytic function on the unit disk . We define a generalized Hilbert-type operator by
,
where a and b are non-negative real numbers. In particular, for a = b = β, becomes the generalized Hilbert operator , and β = 0 gives the classical Hilbert operator . In this article, we find conditions on a and b such that is bounded on Dirichlet-type spaces , 0 < p < 2, and on Bergman spaces , 2 < p < ∞. Also we find an upper bound for the norm of the operator . These generalize...
For various -spaces (1 ≤ p < ∞) we investigate the minimum number of complex-valued functions needed to generate an algebra dense in the space. The results depend crucially on the regularity imposed on the generators. For μ a positive regular Borel measure on a compact metric space there always exists a single bounded measurable function that generates an algebra dense in . For M a Riemannian manifold-with-boundary of finite volume there always exists a single continuous function that generates...
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