Lecture Notes on Functional Analysis

1. Auflage 2026
ISBN: 978-1-041-29275-3
Verlag: Taylor & Francis Ltd

Buch, Englisch, 240 Seiten, Format (B × H): 178 mm x 254 mm

This comprehensive textbook provides a rigorous yet accessible introduction to functional analysis, guiding readers from elementary measure theory through advanced spectral theory. The book is systematically structured across eleven chapters, beginning with Lebesgue measure and progressing through abstract measures, measurable functions, and integration theory before advancing to Banach spaces, Hilbert spaces, and linear operators. Each chapter builds logically upon previous concepts, culminating in spectral theory and applications to Sturm-Liouville equations.

Key Features:

- Progressive pedagogical approach with clear explanations that bridge abstract mathematical concepts and concrete applications through numerous worked examples

- Comprehensive exercise program featuring problems at the end of each section with complete solutions provided at the end of every chapter for self-study and verification •

- Complete coverage spanning from foundational measure theory to advanced functional analysis topics, including Lp spaces, compact operators, and spectral theory in a single, cohesive volume

This self-contained textbook serves as both a structured course text and a pedagogically oriented reference for independent study. The book is ideally suited for undergraduate and graduate students in mathematics, physics, and engineering, as well as instructors seeking a clear, systematic approach to teaching functional analysis.

Zielgruppe

Postgraduate and Undergraduate Advanced

Autoren/Hrsg.

Acquistapace, Paolo

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

1. Lebesgue Measure. 2. Measures. 3. Measurable functions. 4. The Integral. 5. Product Measures. 6. Differentiation. 7. Banach Spaces. 8. Hilbert Spaces. 9. L^p Spaces. 10. Linear Operators 11. Spectral Theory.

Über Autor(innen)

Paolo Acquistapace is an associate professor of Mathematical Analysis at the University of Pisa. For more than forty years he has worked on differential equations, functional analysis and applied problems. He taught several different courses for computer science, biology, geology, mathematics, physics, engineering students, developing a large educational experience.

He taught the course of “Istituzioni di analisi matematica” for several years, researching the most effective pedagogical approach to functional analysis. Retired since 2021, Paolo Acquistapace continues his studies in functional analysis, mainly focusing on its applications to abstract control theory.