04065nam 2200649 450 991078874560332120220328215509.01-4704-0389-7(CKB)3360000000464975(EBL)3114472(SSID)ssj0000973887(PQKBManifestationID)11948273(PQKBTitleCode)TC0000973887(PQKBWorkID)10988937(PQKB)10263302(MiAaPQ)EBC3114472(RPAM)13336380(PPN)195416775(EXLCZ)99336000000046497520030908h20042004 uy| 0engur|n|---|||||txtccrThe role of the spectrum in the cyclic behavior of composition operators /Eva A. Gallardo-Gutiérrez, Alfonso Montes-RodríguezProvidence, Rhode Island :American Mathematical Society,[2004]©20041 online resource (98 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 791"Volume 167, number 791 (first of 5 numbers)."0-8218-3432-0 Includes bibliographical references (pages 79-81).""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""Memoirs of the American Mathematical Society ;no. 791.Function spacesLinear operatorsFunctions of complex variablesHypergeometric functionsFunction spaces.Linear operators.Functions of complex variables.Hypergeometric functions.510 s515/.7246Gallardo-Gutiérrez Eva A.1973-1567057Montes-Rodríguez Alfonso1961-MiAaPQMiAaPQMiAaPQBOOK9910788745603321The role of the spectrum in the cyclic behavior of composition operators3838156UNINA