Zobrazeno 1 - 10
of 104
pro vyhledávání: '"Sola, Alan"'
Given a polynomial $p$ with no zeros in the polydisk, or equivalently the poly-upper half-plane, we study the problem of determining the ideal of polynomials $q$ with the property that the rational function $q/p$ is bounded near a boundary zero of $p
Externí odkaz:
http://arxiv.org/abs/2406.13014
Using real-variable methods, we characterise multipliers for general classes of Hardy--Orlicz spaces, unifying and extending several classical results due to Hardy and Littlewood; Duren and Shields; Paley; and others. Applications of our results incl
Externí odkaz:
http://arxiv.org/abs/2306.09874
Publikováno v:
Ark. Mat. 62 (2024), 331-368
We study Clark measures associated with general two-variable rational inner functions (RIFs) on the bidisk, including those with singularities, and with general $d$-variable rational inner functions with no singularities. We give precise descriptions
Externí odkaz:
http://arxiv.org/abs/2303.11248
Autor:
Sola, Alan
Publikováno v:
Archiv der Mathematik 120, issue 2 (2023), 171-181
We analyze certain compositions of rational inner functions in the unit polydisk $\mathbb{D}^{d}$ with polydegree $(n,1)$, $n\in \mathbb{N}^{d-1}$, and isolated singularities in $\mathbb{T}^d$. Provided an irreducibility condition is met, such a comp
Externí odkaz:
http://arxiv.org/abs/2207.08961
We provide detailed local descriptions of stable polynomials in terms of their homogeneous decompositions, Puiseux expansions, and transfer function realizations. We use this theory to first prove that bounded rational functions on the polydisk posse
Externí odkaz:
http://arxiv.org/abs/2109.07507
Autor:
Sola, Alan, Tully-Doyle, Ryan
Publikováno v:
Annales Polonici Mathematici 128 (2022), 249-273
We examine iteration of certain skew-products on the bidisk whose components are rational inner functions, with emphasis on simple maps of the form $\Phi(z_1,z_2) = (\phi(z_1,z_2), z_2)$. If $\phi$ has degree $1$ in the first variable, the dynamics o
Externí odkaz:
http://arxiv.org/abs/2109.03437
Publikováno v:
Michigan Math. J. 73 (2023), 1021-1057
We analyze the fine structure of Clark measures and Clark isometries associated with two-variable rational inner functions on the bidisk. In the degree (n,1) case, we give a complete description of supports and weights for both generic and exceptiona
Externí odkaz:
http://arxiv.org/abs/2101.00508
Publikováno v:
Ark. Mat. 60 (2022), 231-275
This article is devoted to a study of the Hardy space $H^{\log} (\mathbb{R}^d)$ introduced by Bonami, Grellier, and Ky. We present an alternative approach to their result relating the product of a function in the real Hardy space $H^1$ and a function
Externí odkaz:
http://arxiv.org/abs/2012.02872
Autor:
Sargent, Meredith, Sola, Alan A.
Publikováno v:
Proc. Amer. Math. Soc. 149 (2021), 5321-5330
We obtain closed expressions for weighted orthogonal polynomials and optimal approximants associated with the function $f(z)=1-\frac{1}{\sqrt{2}}(z_1+z_2)$ and a scale of Hilbert function spaces in the unit $2$-ball having reproducing kernel $(1-\lan
Externí odkaz:
http://arxiv.org/abs/2009.01793
Autor:
Sargent, Meredith, Sola, Alan
Publikováno v:
Canadian Journal of Mathematics 74 (2022), 428-456
We discuss the notion of optimal polynomial approximants in multivariable reproducing kernel Hilbert spaces. In particular, we analyze difficulties that arise in the multivariable case which are not present in one variable, for example, a more compli
Externí odkaz:
http://arxiv.org/abs/2002.08790