دانلود کتاب Spectral Theory of Dynamical Systems

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Contents Preface Preface to the Second Edition About the Author Chapter 1 The Hahn-Hellinger Theorem Definitions and the Problem The Case of Multiplicity One, Cyclic Vector Application to Second Order Stochastic Processes Spectral Measures of Higher Multiplicity: A Canonical Example Linear Operators Commuting with Multiplication Spectral Type; Maximal Spectral Type The Hahn-Hellinger Theorem (First Form) The Hahn-Hellinger Theorem (Second Form) Representation of Second Order Stochastic Processes Chapter 2 The Spectral Theorem for Unitary Operators The Spectral Theorem: Multiplicity One Case The Spectral Theorem: Higher Multiplicity Case Chapter 3 Symmetry and Denseness of the Spectrum Spectrum of UT : It is Symmetric Spectrum of UT : It is Dense Examples Chapter 4 Multiplicity and Rank A Theorem on Multiplicity Approximation with Multiplicity N Rank and Multiplicity Chapter 5 The Skew Product The Skew Product: Definition and its Measure Preserving Property The Skew Product: Its Spectrum Chapter 6 A Theorem of Helson and Parry Statement of the Theorem Weak von Neumann Automorphisms and Hyperfinite Actions The Random Cocycle and the Main Theorem Remarks Chapter 7 Probability Measures on the Circle Group Continuous Probability Measures on S^1: They are Dense Gδ Measures Orthogonal to a Given Measure Measures Singular under Convolution and Folding Rigid Measures Chapter 8 Baire Category Theorems of Ergodic Theory Isometries of Lp(X, B, m) Strong Topology on Isometries Coarse and Uniform Topologies on G(m) Baire Category of Classes of Unitary Operators Baire Category of Classes of Non-Singular Automorphisms Baire Category of Classes of Measure Preserving Automorphisms Baire Category and Joinings Chapter 9 Translations of Measures on the Circle A Theorem of Weil and Mackey The Sets A(μ) and H(μ) and Their Topologies Groups Generated by Dense Subsets of A(μ); Their Properties Ergodic Measures on the Circle Group A Theorem on Marginal Measures Chapter 10 B. Host's Theorem Pairwise Independent and Independent Joinings of Automorphisms B. Host's Theorem: The Statement Mixing Implies Multiple Mixing if the Spectrum is Singular B. Host's Theorem: The Proof Chapter 11 L^∞ Eigenvalues of Non-Singular Automorphisms The Group of Eigenvalues and Its Polish Topology The Group e(T ) is σ-compact The Group e(T ) is Saturated Chapter 12 Generalities on Systems of Imprimitivity Spectral Measures and Group Actions Cocycles; Systems of Imprimitivity Irreducible Systems of Imprimitivity Transitive Systems Transitive Systems on R Chapter 13 Dual Systems of Imprimitivity Compact Group Rotations; Dual Systems of Imprimitivity Irreducible Dual Systems; Examples The Group of Quasi-Invariance; Its Topology The Group of Quasi-Invariance; It is an Eigenvalue Group Extensions of Cocycles Chapter 14 Saturated Subgroups of the Circle Group Saturated Subgroups of S^1 Relation to Closures and Convex Hulls of Characters σ-Compact Saturated Subgroups; H2 Groups Chapter 15 Riesz Products As Spectral Measures Dissociated Trigonometric Polynomials Classical Riesz Products and a Theorem of Peyriére Riesz Products and Dynamics Generalised Riesz Products Maximal Spectral Types of Rank One Automorphisms Examples and Remarks The Non-Singular Case, Proof of Theorem 15.18, and Further Remarks Rank One Automorphisms: Their Group of Eigenvalues Preliminary Calculations The Eigenvalue Group: Osikawa Criterion Restatement of Theorem 15.50 The Eigenvalue Group: Structural Criterion An Expression for dσα/dσ , α ∈ e(T) Chapter 16 Additional Topics Bounded Functions with Maximal Spectral Type A Result on Mixing A Result On Multiplicity Combinatorial and Probabilistic Lemmas Rank One Automorphisms by Construction Ornstein's Class of Rank One Automorphisms Mixing Rank One Automorphisms Chapter 17 Calculus of Generalized Riesz Products Generalized Riesz Products and their Weak Dichotomy Outer Polynomials and Mahler Measure A Formula for Radon Nikodym Derivative A Conditional Strong Dichotomy and Other Discussion Non-Singular Rank One Maps and Generalized Riesz Products Generalized Riesz Products of Dynamical Origin Zeros of Polynomials References Index