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Showing 1 to 19 of 19 for “"Hardy space"”.
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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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Hardy-space Function Theory on Finitely Connected Planar Domains
Hardy space scalar theory on the disk is now classical. Some extensions have been done, one of them is the approach done by Donald Sarason using Laurent series. We present the more complicated function theory, without the use of either power series or Laurent series, for finitely-connected planar …
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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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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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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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Towards a Connection between Linear Embedding and the Poincaré Functional Equation.
… consider linear embedding schemes in a classical Hardy space.</p>
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Properties of truncated Toeplitz operators
… or TTOs) on backward shift invariant subspaces of the Hardy space of the unit disc. Specifically we discuss when the product of two TTOs is itself a TTO, finding an equivalent to a similar result of Brown and Halmos for ordinary Toeplitz operators. This leads us to investigate the …
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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
… a full-range simply-invariant shift-invariant subspace <i>M</i> of the vector-valued <i>L<sup>2</sup></i> space on the unit circle, the classical Beurling-Lax-Halmos (BLH) theorem obtains a unitary operator-valued function <i>W</i> so that <i>M</i> may be represented as the image of of the Hardy …
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Closed Range Composition Operators on BMOA
… all p ∈ (0,∞). </p> <p>Let B denote the Bloch space, let H2 denote the Hardy space. We show that if Cφ is closed range on B or on H2 then it is also closed range on BMOA. Closed range composition operators Cφ : B → BMOA are also characterized. Laitila found the isometries among composition …
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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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Estimates on Oscillatory Singular Integral Operators
… to the operator’s behavior over any function space. Studies on such operators are rooted in the deep theories developed by Fourier, Calder´on, Zygmund, and Stein. In this work we show results on a new oscillatory singular integral operator with Calder´on-Zygmund kernel and a generalized phase …
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Several Problems Concerning Multivariate Functions and Associated Operators
… provided, which uses special shift-invariant subspaces of the Hardy space. These shift-invariant subspaces are specific cases of Hilbert spaces that can be defined from Agler decompositions and their properties are analyzed. More specific results are obtained for certain classes of polynomials …
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On the Integrability of Derivatives of Holomorphic and M-Subharmonic Inner Functions In the Unit Ball of Cn
… and p > 0 then Apa denotes the weighted Bergman space of all holomorphic functions weighted by (1-|z|^2)a and for 0 < q < 1, set Bq := A1(n/q)-n-1. For p > 0 let Hp denote the usual Hardy space of holomorphic functions on the ball. </p> <p>In this dissertation, we consider derivatives of inner …
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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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Polynomial approximation and Carleson measures on a general domain and equivalence classes of subnormal operators
… the set of analytic polynomials, is dense in the Hardy space H<sup>t</sup>(G) or the Bergman space L<sup>t</sup><sub>n</sub>G, where G is a bounded domain and t ∈ [1,∞). Characterizations of special domains are also given. In Chapter 3 we generalize the definition of a Carleson measure to an …
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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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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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Toeplitzness of Composition Operators and Parametric Toeplitzness
<p>This thesis is based on some problems posed in \cite{BaHa} and\cite{NazarovShapiro}, and in some cases, we find thesolutions and investigate their properties.</p><p>Chapter 1 presents the prerequisites for the rest of the chapters.These materials can be found with more details in the books cited …
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A STUDY OF DE BRANGES - ROVNYAK AND DIRICHLET SPACES
… thesis is devoted to the study of certain spaces of analytic functions on the unit disk $\mathbb{D}$ of the complex plain, $\mathbb{D}:=\{z\in\mathbb{C}\colon |z|<1\}$. This work lies in the intersection between complex analysis, operator theory and harmonic analysis. In particular, we are …