Author | Nikol'skiฤญ, Nikolaฤญ K. author |
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Title | Treatise on the Shift Operator [electronic resource] : Spectral Function Theory / by Nikolaฤญ K. Nikol'skiฤญ |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1986 |
Connect to | http://dx.doi.org/10.1007/978-3-642-70151-1 |
Descript | XI, 491 p. online resource |
Introductory Lecture. What This Book is About -- 1. Basic Objects -- 2. The Functional Model -- 3. The Details of the Plan -- 4. Concluding Remarks -- Lecture I. Invariant Subspaces -- 1. The Fundamental Theorem -- 2. The Inner-Outer Factorization -- 3. The Arithmetic of Inner Functions -- 4. The Adjoint Operators S* -- Supplements and Bibliographical Notes -- 5. Invariant Subspaces -- 6. The Shift of Arbitrary Multiplicity -- 7. Concluding Remarks -- Lecture II. Individual Theorems for the Operator S* -- 1. Pseudocontinuation of H2-Functions and S*-Cyclicity -- 2. Approximation by Rootspaces -- Supplements and Bibliographical Notes -- 3. More General Capacities -- 4. The Operator SE* -- 5. Concluding Remarks -- Lecture III. Compressions of the Shift and the Spectra of Inner Functions -- 1. The Spectrum of an Operator and the Spectrum of a Function -- 2. Functional Calculus and Derivation of Theorem LM -- 3. The Spectrum of the Operator ?(T) -- Supplements and Bibliographical Notes -- 4. The Cyclic Vectors for the Operators T = PS and T* -- 5. A Calculus for Completely Non-Unitary Contractions -- 6. The Class C0 -- 7. The Characteristic Function and the Spectrum -- 8. Concluding Remarks -- Lecture IV. Decomposition into Invariant Subspaces -- 1. Spectral Synthesis -- 2. Spectral Subspaces -- 3. Unicellular Operators -- Supplements and Bibliographical Notes -- 4. On Invariant Subspaces -- 5. Synthesis for C0-Operators -- 6. On Spectral Subspaces -- 7. Concerning Unicellular Operators -- 8. Concluding Remarks -- Lecture V. The Triangular Form of the Truncated Shift -- 1. Pure Point Spectrum -- 2. Continuous Singular Spectrum -- 3. Atomic Singular Spectrum -- 4. The General Case and Applications -- Supplements and Bibliographical Notes -- 5. Triangular Representations of More General Operators -- 6. Concluding Remarks -- Lecture VI. Bases and Interpolation (Statement of the Problem) -- 1. Riesz Bases -- 2. Interpolation -- 3. Spectral Projections and Unconditional Convergence -- Supplements and Bibliographical Notes -- 4. Bases of Subspaces -- 5. Bases of Eigenspaces -- 6. Concluding Remarks -- Lecture VII. Bases and Interpolation (Solution) -- 1. Carleson Measures -- 2. Proof of the Theorem on Bases and Interpolation -- 3. Analysis of Carleson's Condition (C) -- Supplements and Bibliographical Notes -- 4. Carleson Series -- 5. Remarks on Imbedding Theorems -- 6. Concluding Remarks -- Lecture VIII. Operator Interpolation and the Commutant -- 1. Interpolation by Bounded Analytic Functions -- 2. The Proof of Sarason's Theorem -- 3. Compact Operators in T?? -- Supplements and Bibliographical Notes -- 4. The Multiplier Method and the Operator Calculus -- 5. Summation Bases -- 6. Hankel Operators and Angles Between Subspaces -- 7. Concluding Remarks -- Lecture IX. Generalized Spectrality and Interpolation of Germs of Analytic Functions -- 1. Generalized Spectrality -- 2. Non-Classical Interpolation in H? and Bases -- 3. The Rรดle of the Uniform Minimality -- 4. Interpolation of Germs of Analytic Functions -- 5. Splitting and Blocking of Rootspaces -- 6. Spectrality and B0-Spectrality -- 7. Concluding Remarks -- Lecture X. Analysis of the Carleson-Vasyunin Condition -- 1. An Estimate for the Angle in Terms of Representing Measures -- 2. Bases of Rootspaces -- 3. Stolzian Spectrum -- 4. Singular Discrete Spectrum -- 5. Counterexamples -- 6. Concluding Remarks -- Lecture XI. On the Line and in the Halfplane -- 1. The Invariant Subspaces -- 2. Bases of Exponentials -- 3. Concluding Remarks -- Appendix 4. Essays on the Spectral Theory of Hankel and Toeplitz Operators -- (For detailed contents see page 300) -- (For detailed contents see page 400) -- List of Symbols -- Author Index