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Showing 1 to 14 of 14 for “"Hardy Spaces"”.
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Poletsky-Stessin Hardy Spaces on the Unit Disk
… boundary values) led to the appearance of Hardy spaces $H^p(\mathbb{D})$, $p\ge1$. If a function lies in a Hardy space then its boundary values can be defined and its values on $\mathbb{D}$ can be obtained using standard Cauchy or Poisson formulas.</p> <p> The theory of Hardy spaces …
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Blaschke Decompositions on Weighted Hardy Spaces and the Unwinding Series
… the study of Blaschke decompositions on weighted Hardy spaces was initiated by Coifman and Steinerberger, under the assumption that the complex valued function F has an analytic extension to D_1+ε for some ε > 0. This provided bounds on weighted Hardy norms involving a single zero, α ∈ D, of F and …
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Spectral Decompositions of Isometries on Hardy Spaces of the Disk and the Torus
… and (single) power-bounded operators on UMD spaces.
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Discrete Littlewood-Paley-Stein Theory And Wolff Potentials On Homogeneous Spaces And Multi-Parameter Hardy Spaces
… new atomic decomposition of the multi-parameter Hardy spaces of homogeneous type and obtain the associated $H^p-L^p$ and $H^p-H^p$ boundedness criterions for singular integral operators. On the other hand, we compare the Wolff and Riesz potentials on spaces of homogenous type, followed by a …
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A Beurling Theorem for Noncommutative Hardy Spaces Associated with a Semifinite von Neumann Algebra with Various Norms
… prove Beurling-type theorems for H-invariant spaces in relation to a semifinite von Neu-mann algebra M with a semifinite, faithful, normal tracial weight τ, using an extension of Arveson’s non-commutative Hardy space H-. First we prove a Beurling-Blecher-Labuschagne theorem for H-invariant …
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Kernels of adjoints of composition operators on Hilbert spaces of analytic functions
… composition operator and its kernel in weighted Hardy spaces, in particular, the classical Hardy, Bergman, and Dirichlet spaces. In 2006, Cowen and Gallardo-Gutiérrez laid the groundwork for an explicit formula for the adjoint of a composition operator with rational symbol acting on the Hardy …
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Intertwining relations, commutativity and orbits
… properties of linear operators on Banach spaces and the Invariant Subspace Problem. As a consequence, the research on the Theory of Hyperclicity has increased considerably. In this manuscript, we characterize the hypercyclicity of the Cesàro means of higher-order on Banach spaces. We prove …
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Holomorphic Hardy Space Representations for Convex Domains in Cn
<p>This thesis deals with Hardy Spaces of holomorphic functions for a domain in several complex variables, that is, when the complex dimension is greater than or equal to two. The results we obtain are analogous to well known theorems in one complex variable. The domains we are concerned with are …
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Banach Spaces of Analytic Vector-valued Functions
… involving matrix-valued and vector-valued Hardy spaces on the unit disc ID and its boundary T in the complex plane. The first part of the thesis looks at the factorization of square matrix-valued boundary functions, beginning with spectral factorization in Chapter 2. Then ideas involving …
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Parametric Dynamical Systems: Transient Analysis and Data Driven Modeling
Dynamical systems are a commonly used and studied tool for simulation, optimization and design. In many applications such as inverse problem, optimal control, shape optimization and uncertainty quantification, those systems typically depend on a parameter. The need for high fidelity in the modeling …
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Hardy Space Properties of the Cauchy Kernel Function for a Strictly Convex Planar Domain
<p>This work is based on a paper by Edgar Lee Stout, where it is shown that for every strictly pseudoconvex domain $D$ of class $C^2$ in $\mathbb{C}^N$, the Henkin-Ram\'irez Kernel Function belongs to the Smirnov class, $E^q(D)$, for every $q\in(0,N)$.</p> <p>The main objective of this dissertation …
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Beurling-Lax Representations of Shift-Invariant Spaces, Zero-Pole Data Interpolation, and Dichotomous Transfer Function Realizations: Half-Plane/Continuous-Time Versions
… may be represented as the image of of the Hardy space <i>H<sup>2</sup></i> on the disc under multiplication by <i>W</i>. The work of Ball-Helton later extended this result to find a single function representing a so-called dual shift-invariant pair of subspaces <i>(M,M<sup>Ã </sup>)</i> …