Adam Bobrowski

Functional Analysis Revisited

An Essay on Completeness

• Broschiertes Buch

Produktbeschreibung

Suitable for graduate students, this book reviews basic functional analysis focusing on the fundamental notion of completeness, demonstrating how it lies at the core of our understanding of mathematics. The theory is introduced step by step using examples and exercises; applications to other branches of mathematics are discussed in depth.

Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 250
• Erscheinungstermin: 4. Juli 2024
• Englisch
• ISBN-13: 9781009430890
• ISBN-10: 1009430890
• Artikelnr.: 70147151

Autorenporträt

Adam Bobrowski is a professor in the Department of Mathematics at Lublin University of Technology, Poland. He was awarded the Hugo Steinhaus Prize for his achievements in analyzing mathematical models of biological reality and has authored more than 70 scientific papers and six books. His works include 'Functional Analysis for Probability and Stochastic Processes' (2005), 'Convergence of One-Parameter Operator Semigroups' (2016), and 'Generators of Markov Chains' (2020).

Inhaltsangabe

Introduction
1. Complete metric spaces
2. Banach's principle
3. Picard's theorem
4. Banach spaces
5. Renewal equation in the McKendrick-von Foerster model
6. Riemann integral for vector-valued functions
7. The Stone-Weierstrass theorem
8. Norms do differ
9. Hilbert spaces
10. Complete orthonormal sequences
11. Heat equation
12. Completeness of the space of operators
13. Working in L(X)
14. The Banach-Steinhaus theorem and strong convergence
15. We go deeper, deeper we go (into the structure of complete spaces)
16. Semigroups of operators
Appendix. Two consequences of the Hahn-Banach theorem
References
Index.