Polynomial inequalities for non-commuting operators
We prove an inequality for polynomials applied in a symmetric way to non-commuting operators.
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arXiv subjects
John E. McCarthy
Publications and source records attributed to John E. McCarthy.
Cusp Algebras
We consider simple cusp algebras, that is certain subalgebras of the algebra of holomorphic functions on a disk that are annihilated by some distributions living on a singleton. We determine when these algebras can be holized in two dimensions, and when these holizations are globally biholomorphic.
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Hyperbolic algebraic and analytic curves
A hyperbolic algebraic curve is a bounded subset of an algebraic set. We study the function theory and functional analytic aspects of these sets. We show that their function theory can be described by finite codimensional subalgebras of the holomorphic functions on the desingularization. We show that classical analytic techniques, such as interpolation, can be used to answer geometric questions about the existence of biholomorphic maps. Conversely, we show that the algebraic-geometric viewpoint leads to interesting questions in classical analysis.
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Norm preserving extensions of holomorphic functions from subvarieties of the bidisk
A basic result in the theory of holomorphic functions of several complex variables is the following special case of the work of H. Cartan on the sheaf cohomology on Stein domains ([10], or see [14] or [16] for more modern treatments).
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Hilbert spaces of Dirichlet series
We consider various Hilbert spaces of Dirichlet series whose norms are given by weighted $\ell^2$ norms of the Dirichlet coefficients. We characterize the multiplier algebras for some of these spaces.
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Best approximation in the mean by analytic and harmonic functions
We consider the problem of finding the best harmonic or analytic approximant to a given function. We discuss when the best approximant is unique, and what regularity properties the best approximant inherits from the original function. All our approximations are done in the mean with respect to Lebesgue measure in the plane or higher dimensions.
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On Pisier's Construction
A classical proof of Pisier's construction of a polynomially bounded operator not similar to a contraction is given.
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