Tools for infinite dimensional analysis. (2020)

• Record Type: Book
• Further Information: Note: Jeremy J. Becnel.
• Authors: Becnel, Jeremy J
• Contents: 1. Schwartz Space. 1.1. The Schwartz Space. 1.2. The Schwartz Norm Topology. 1.3. Fourier Transform. 1.4. Physical Context. 1.5. Orthonormal Basis, Creation, and Annihilation Operators in L²(R). 1.6. Number Operator and the Spaces Sp(R). 1.7. The Projective Limit Topology on S(R). 1.8. L² norms on S(R). 1.9. Equivalence of the Topologies. 1.10. The Sequence Space. 1.11. Multidimensional. 2. Nuclear Spaces. 2.1. Topological Vector Spaces. 2.2. Countably-Normed Spaces. 2.3. Nuclear Space Structure. 2.4. Nuclear Space Construction from a Hilbert Space and an Operator. 3. Dual Space. 3.1. Linear Functionals. 3.2. Dual Space. 3.3. The Dual of a Nuclear Space. 3.4. Topologies on Hʼ. 3.5. Reflexivity. 3.6. Convergence and Completeness in Hʼ. 3.7. Properties of the Topology on H' and H_p. 3.8. Inductive Limit Topology. 3.9. Sequential Space. 3.10. First Countability (Lack Thereof). 3.11. Summary. 3.12. Abstract Kernel Theorem. 3.13. White Noise Dual. 3.14. Schwartz Space Dual. 3.15. Boxes and Continuous Functions. 4. Probability Theory. 4.1. Probability Theory Fundamentals. 4.2. Product Sigma Algebras in Infinite Dimensions. 4.3. Sigma Algebras on the Dual of a Nuclear Space. 4.4. Probability Measures on Infinite Dimensional Spaces. Appendix: Banach and Hilbert Spaces.
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2020
• Extent: 1 online resource
• Subjects: 515.73; Dimensional analysis; Linear topological spaces
• Languages: English
• ISBNs: 9781000328288; 9781000328264; 9781000328271; 9781003088974
• Related ISBNs: 9780367543662
• Notes: Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.