2007
DOI: 10.1515/crelle.2007.033
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Interpolation in semigroupoid algebras

Abstract: ABSTRACT. A seminal result of Agler characterizes the so-called Schur-Agler class of functions on the polydisk in terms of a unitary colligation transfer function representation. We generalize this to the unit ball of the algebra of multipliers for a family of test functions over a broad class of semigroupoids. There is then an associated interpolation theorem. Besides leading to solutions of the familiar Nevanlinna-Pick and Carathéodory-Fejér interpolation problems and their multivariable commutative and nonc… Show more

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Cited by 22 publications
(39 citation statements)
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“…(20) in the seventh. Now use linearity and the fact that the linear span of elements like F is dense in L 2 (μ) ⊗ 2 to finish the proof of the first part of Lemma 7.2.…”
Section: Ieotmentioning
confidence: 99%
See 2 more Smart Citations
“…(20) in the seventh. Now use linearity and the fact that the linear span of elements like F is dense in L 2 (μ) ⊗ 2 to finish the proof of the first part of Lemma 7.2.…”
Section: Ieotmentioning
confidence: 99%
“…Results going back to [5] and including [3,4,7,10,15,16,19,20] among others view the starting point for Agler-Pick interpolation as a collection of functions Ψ, called test functions. Roughly speaking one constructs an operator algebra whose norm is as large as possible subject to the condition that each ψ ∈ Ψ is contractive.…”
Section: Introductionmentioning
confidence: 99%
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“…Results going back to [1] and including [2,5,6,10,11,14,15] among others view the starting point for Agler-Pick interpolation as a collection of functions Ψ. Roughly speaking one then constructs an operator algebra whose norm is as large as possible subject to the condition that each ψ ∈ Ψ is contractive.…”
Section: Introductionmentioning
confidence: 99%
“…The corresponding AglerSchur class, or Ψ-Agler-Schur class, is then the unit ball of this operator algebra and interpolation is within this class. While much of the work assumes and exploits to some extent analytic structure, it turns out that much goes through independent of analyticity [2,14]. Indeed, the reproducing kernel Hilbert spaces impose an ersatz analytic structure.…”
Section: Introductionmentioning
confidence: 99%