Role of the Spectrum in the Cyclic Behavior of Composition Operators.

Intro -- Contents -- Preface -- Chapter 1. Introduction and Preliminaries -- Weighted Hardy spaces -- The Dirichlet space -- The Hardy space -- Functional Hilbert spaces -- Composition operators -- Weighted Dirichlet spaces -- Equivalent norms on weighted Dirichlet spaces -- Linear fractional maps -- Iterates -- The Comparison Principle -- Main results -- Table I -- Table II -- Acknowledgment -- Chapter 2. Linear Fractional Maps with an Interior Fixed Point -- Non-elliptic linear fractional maps with an exterior fixed point -- Elliptic automorphism -- Interior and boundary fixed point -- Hypercyclicity -- The hyperbolic automorphism -- The Hypercyclic Criterion -- A Beurling type theorem -- The Inner Product Criterion -- Invariant subspaces of finite codimension -- Chapter 3. Non Elliptic Automorphisms -- Hypercyclicity -- The parabolic automorphism -- The hyperbolic automorphism -- The failure of the spectrum -- The eigenfunctions of C[sub([omitted])] [sub([omitted])] with a parabolic automorphism -- Cyclicity -- The Dirichlet space of the upper half plane -- The Hardy space of the upper half plane -- A Paley-Wiener Theorem for D[sub(π)] -- The parabolic automorphism -- The hyperbolic automorphism -- Chapter 4. The Parabolic Non Automorphism -- Cyclicity -- Zeros of weighted Dirichlet functions -- Non hypercyclicity -- An appetizer -- The spectrum of C[sub([omitted])] -- The eigenfunctions form a spanning set -- Renorming S[sub(v)] -- Isometric functional Hilbert spaces -- A complete orthogonal system of L[sup(2)] (R[sup(+)],dt/t) -- The extension of the isometries -- The Laguerre polynomials -- Chapter 5. Supercyclic Linear Fractional Composition Operators -- The easy part -- The parabolic non-automorphism -- The Angle Criterion -- The adjoint of C[sub([omitted])] -- A three term recurrence formula -- An integration formula -- Endnotes.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.