The Dirichlet space: a survey.
Arcozzi, Nicola; Rochberg, Richard; Sawyer, Eric T.; Wick, Brett D. — 2011
The New York Journal of Mathematics [electronic only]
The Dirichlet space: a survey.
Simultaneous stabilization in
We study the problem of simultaneous stabilization for the algebra . Invertible pairs , j = 1,..., n, in a commutative unital algebra are called simultaneously stabilizable if there exists a pair (α,β) of elements such that is invertible in this algebra for j = 1,..., n. For n = 2, the simultaneous stabilization problem admits a positive solution for any data if and only if the Bass stable rank of the algebra is one. Since has stable rank two, we are faced here with a different situation....
A remark on the multipliers on spaces of Weak Products of functions
If H denotes a Hilbert space of analytic functions on a region Ω ⊆ Cd , then the weak product is defined by [...] We prove that if H is a first order holomorphic Besov Hilbert space on the unit ball of Cd , then the multiplier algebras of H and of H ⊙ H coincide.
Doubly commuting submodules of the Hardy module over polydiscs
In this note we establish a vector-valued version of Beurling’s theorem (the Lax-Halmos theorem) for the polydisc. As an application of the main result, we provide necessary and sufficient conditions for the “weak” completion problem in .
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