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Search: MSC category 46E22 ( Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32] )

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1. CMB 2017 (vol 61 pp. 704)

Bénéteau, Catherine Anne; Fleeman, Matthew C.; Khavinson, Dmitry S.; Seco, Daniel; Sola, Alan
 Remarks on Inner Functions and Optimal Approximants We discuss the concept of inner function in reproducing kernel Hilbert spaces with an orthogonal basis of monomials and examine connections between inner functions and optimal polynomial approximants to $1/f$, where $f$ is a function in the space. We revisit some classical examples from this perspective, and show how a construction of Shapiro and Shields can be modified to produce inner functions. Keywords:inner function, reproducing Kernel Hilbert Space, operator-theoretic function theoryCategories:46E22, 30J05

2. CMB 2014 (vol 58 pp. 9)

Chavan, Sameer
 Irreducible Tuples Without the Boundary Property We examine spectral behavior of irreducible tuples which do not admit boundary property. In particular, we prove under some mild assumption that the spectral radius of such an $m$-tuple $(T_1, \dots, T_m)$ must be the operator norm of $T^*_1T_1 + \cdots + T^*_mT_m$. We use this simple observation to ensure boundary property for an irreducible, essentially normal joint $q$-isometry provided it is not a joint isometry. We further exhibit a family of reproducing Hilbert $\mathbb{C}[z_1, \dots, z_m]$-modules (of which the Drury-Arveson Hilbert module is a prototype) with the property that any two nested unitarily equivalent submodules are indeed equal. Keywords:boundary representations, subnormal, joint p-isometryCategories:47A13, 46E22

3. CMB 2011 (vol 56 pp. 400)

Prunaru, Bebe
 A Factorization Theorem for Multiplier Algebras of Reproducing Kernel Hilbert Spaces Let $(X,\mathcal B,\mu)$ be a $\sigma$-finite measure space and let $H\subset L^2(X,\mu)$ be a separable reproducing kernel Hilbert space on $X$. We show that the multiplier algebra of $H$ has property $(A_1(1))$. Keywords:reproducing kernel Hilbert space, Berezin transform, dual algebraCategories:46E22, 47B32, 47L45
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