The role of the spectrum in the cyclic behavior of composition operators / / Eva A. Gallardo-Gutiérrez, Alfonso Montes-Rodríguez

• Record Nr.: UNINA9910478894103321
• Autore: Gallardo-Gutieŕrez Eva A. <1973->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , [2004]; ©2004
• ISBN: 1-4704-0389-7
• Descrizione fisica: 1 online resource (98 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 791
• Disciplina: 510 s; 515/.7246
• Soggetti: Function spaces; Linear operators; Functions of complex variables; Hypergeometric functions; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "Volume 167, number 791 (first of 5 numbers)."
• Nota di bibliografia: Includes bibliographical references (pages 79-81).
• Nota di contenuto: ""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(Ï€)]""""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""; ""Bibliography""