Chapman and Hall/CRC
454 pages | 8 B/W Illus.
Basic Analysis III: Mappings on Infinite Dimensional Spaces is intended as a first course in abstract linear analysis. This textbook cover metric spaces, normed linear spaces and inner product spaces, along with many other deeper abstract ideas such a completeness, operators and dual spaces. These topics act as an important tool in the development of a mathematically trained scientist.
"Mathematics is fortunate to be populated by bright practitioners. Nonetheless, amongst these we are fortunate to have rare individuals who are wise. Professor Peterson is a member of this distinguished group. His works clearly demonstrate the importance of a long career of research and teaching where he combines the two perspectives of: (1) clearly understanding the needs of diverse readers for clear exposition that scaffolds their exposure to complex material with a transparency about both where they are going and what the utility is of what they are currently reading; and, (2) the benefits of having used the mathematics under consideration in so many diverse applications. The masterly synthesis of so much complex material by a single individual is a superb achievement which will reward serious readers with insight, surprise, and breadth as well as depth."
—Professor John R. Jungck, University of Delaware
I. Introduction II. Metric Spaces. 2. Metric Spaces. 3. Completing a Metric Space. III. Normed Linear Spaces. 4. Vector Spaces. 5. Normed Linear Spaces. 6. Linear Operators on Normed Spaces. IV. Inner Product Spaces. 7. Inner Product Spaces. 8. Hilbert Spaces. 9. Dual Spaces. 10. Hahn - Banach Results. 11. More About Dual Spaces. 12. Some Classical Results. V. Operators. 13. Sturm–Liouville Operators. 14. Self Adjoint Operators. VI. Topics in Applied Modeling. 15. Fields and Charges on a Set. 16. Games. VII. Summing It All Up. VIII. References. IX. Detailed Indices.