Theory of Functions of a Real Variable by Shlomo Sternberg
Theory of Functions of a Real Variable - Table of Contents
- 1. The Topology of Metric Spaces
- 2. Hilbert Spaces and Compact Operators
- 3. The Fourier Transform
- 4. Measure Theory
- 5. The Lebesgue Integral
- 6. The Daniell Integral
- 7. Wiener Measure, Brownian Motion and White Noise
- 8. Haar Measure
- 9. Banach Algebras and the Spectral Theorem
- 10. The Spectral Theorem
- 11. Stone’s Theorem
- 12. More About the Spectral Theorem
- 13. Scattering Theory
What You Will Learn in Theory of Functions of a Real Variable
Theory of Functions of a Real Variable by Shlomo Sternberg is a masterclass in modern mathematical analysis, bridging classical real variables with advanced geometric and functional frameworks. Written by a renowned mathematician and physicist, the text covers core graduate-level topics including measure and integration, topological and metric spaces, Banach and Hilbert spaces, spectral theory, and the foundations of differential forms and calculus on manifolds.
This book serves as an invaluable guide for graduate students in mathematics and mathematical physics who want to build a deep, rigorous understanding of the mathematical structures underpinning analysis and geometry. Sternberg combines profound theoretical depth with elegant conceptual frameworks, ensuring readers develop powerful analytical reasoning skills.
Due to its authoritative presentation and unique perspective connecting analysis with geometry and physics, it is widely recognized as an outstanding reference text for graduate real analysis and modern mathematical physics. Rather than focusing solely on computational techniques, it equips learners with the advanced theoretical machinery necessary for research in analysis, differential geometry, and theoretical physics.
Book Details & Specifications
Title:
Theory of Functions of a Real Variable by Shlomo Sternberg
Publisher:
N\A
Year:
2005
Pages:
393
Type:
PDF
Language:
English
ISBN-10 #:
1616100788
ISBN-13 #:
978-1616100780
License:
External Educational Resource
Amazon:
Amazon
About the Author: Shlomo Zvi Sternberg
The author Shlomo Zvi Sternberg
(1936–2024) was a distinguished American mathematician and professor at Harvard University, renowned for his foundational contributions to differential geometry, celestial mechanics, mathematical physics, and group theory.
Through Theory of Functions of a Real Variable, Sternberg successfully synthesized rigorous analysis with geometric intuition into a clear, unified text. His profound mathematical perspective makes this book a masterpiece resource for advanced mathematical analysis.
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