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Linear Dynamical Systems on Hilbert Spaces: Typical Properties and Explicit Examples (Memoirs of the American Mathematical Society) by Sophie Grivaux; Étienne Matheron; Quentin Menet is a nonfiction available to read on EtoBox.
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Cover Title page Chapter 1. Introduction 1. General overview 2. Background and notations 2.1. Transitivity, mixing and weak mixing 2.2. Chaos 2.3. Ergodic-theoretic properties 2.4. Frequent hypercyclicity and 𝒰-frequent hypercyclicity 2.5. Properties related to eigenvalues 2.6. Distributional chaos 2.7. The parameter 𝑐(𝑇) 2.8. A last notation 3. Organization of the monograph Chapter 2. Typical properties of hypercyclic operators 1. The strong and strong^{*} topologies 1.1. Why 𝚂𝙾𝚃 and 𝚂𝙾𝚃*? 2. How to prove density results 3. Construction of mixing operators, and density of \gsmxh 4. Topological weak mixing and topological mixing 4.1. Some illustrations 5. Hypercyclic operators without eigenvalues 6. Hypercyclic operators without invariant measures 7. Densely distributionally chaotic operators 8. Summary Chapter 3. Descriptive set-theoretic issues 1. Complexity of the families 𝑇𝑀𝐼𝑋_{𝑀}()̉, \cmh, 𝑈𝐹𝐻𝐶_{𝑀}()̉∩𝐶𝐻_{𝑀}()̉ and 𝑈𝐹𝐻𝐶_{𝑀}()̉ 1.1. Complexity of 𝑇𝑀𝐼𝑋_{𝑀}()̉ 1.2. Complexity of \cmh 1.3. Complexity of 𝑈𝐹𝐻𝐶_{𝑀}()̉ and 𝑈𝐹𝐻𝐶_{𝑀}()̉∩𝐶𝐻_{𝑀}()̉ 2. Some non-Borel sets in \bmh Chapter 4. Ergodicity for upper-triangular operators 1. Definition
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- Author
- Sophie Grivaux; Étienne Matheron; Quentin Menet
- Publisher
- American Mathematical Society
- Published
- 2021
- Language
- EN
- ISBN
- 9781470446635
- Category
- nonfiction
- Subjects
- Computer Science, Mathematics, Programming
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