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Functional Analysis Revisited - Adam Bobrowski

Functional Analysis Revisited

An Essay on Completeness

(Autor)

Buch | Softcover
250 Seiten
2024
Cambridge University Press (Verlag)
978-1-009-43089-0 (ISBN)
CHF 69,80 inkl. MwSt
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.
'Functional Analysis Revisited' is not a first course in functional analysis – although it covers the basic notions of functional analysis, it assumes the reader is somewhat acquainted with them. It is by no means a second course either: there are too many deep subjects that are not within scope here. Instead, having the basics under his belt, the author takes the time to carefully think through their fundamental consequences. In particular, the focus is on the notion of completeness and its implications, yet without venturing too far from areas where the description 'elementary' is still valid. The author also looks at some applications, perhaps just outside the core of functional analysis, that are not completely trivial. The aim is to show how functional analysis influences and is influenced by other branches of contemporary mathematics. This is what we mean by 'Functional Analysis Revisited.'

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).

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.

Erscheinungsdatum
Zusatzinfo Worked examples or Exercises
Verlagsort Cambridge
Sprache englisch
Maße 153 x 228 mm
Gewicht 380 g
Themenwelt Mathematik / Informatik Mathematik Analysis
ISBN-10 1-009-43089-0 / 1009430890
ISBN-13 978-1-009-43089-0 / 9781009430890
Zustand Neuware
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