A Primer on Hilbert Space Theory

Linear Spaces, Topological Spaces, Metric Spaces, Normed Spaces, and Topological Groups
Buch | Softcover
XVII, 255 Seiten
2016 | 1. Softcover reprint of the original 1st ed. 2015
Springer International Publishing (Verlag)
978-3-319-35351-7 (ISBN)

Lese- und Medienproben

A Primer on Hilbert Space Theory - Carlo Alabiso, Ittay Weiss
64,19 inkl. MwSt
This introduction to Hilbert space will equip the reader for more demanding further study. It builds a pedagogic bridge between the rigorous style of mathematics and the more practical perspective of physicists.

This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case. Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude.

With respect to the original lectures, the mathematical flavor in all subjects has been enriched. Moreover, a brief introduction to topological groups has been added in addition to exercises and solved problems throughout the text. With these improvements, the book can be used in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.

Prof. Carlo Alabiso obtained his Degree in Physics at Milan University and then taught at Parma University, Parma, Italy for more than 40 years (with a period spent as a research fellow at the Stanford Linear Accelerator Center and at Cern, Geneva). His teaching encompassed topics in quantum mechanics, special relativity, field theory, elementary particle physics, mathematical physics, and functional analysis. His research fields include mathematical physics (Pad/' e} approximants), elementary particle physics (symmetries and quark models), and statistical physics (ergodic problems), and he has published articles in a wide range of national and international journals as well as the previous Springer book (with Alessandro Chiesa), Problemi di Meccanica Quantistica non Relativistica. Dr. Ittay Weiss completed his BSc and MSc studies in Mathematics at the Hebrew University of Jerusalem and he obtained his PhD in mathematics from Universiteit Utrecht in the Netherlands. He spent an additional three years in Utrecht as an assistant professor of mathematics, teaching mathematics courses across the entire undergraduate spectrum both at Utrecht University and at the affiliated University College Utrecht. He is currently a mathematics lecturer at the University of the South Pacific. His research interests lie in the fields of algebraic topology and operad theory, as well as the mathematical foundations of analysis and generalizations of metric spaces.

1 Introduction and Preliminaries.- 2 Linear Spaces.- 3 Topological Spaces.- 4 Metric Spaces.- 5 Normed Spaces.- 6 Topological Groups.- 7 Solved Problems.

"This book introduces essential ideas and results of Hilbert space and linear operator theory to beginners in quantum physics. ... The textbook is suitable for advanced undergraduate or introductory graduate courses for both physics and mathematics students." (Michael Frank, Mathematical Reviews, August, 2015)

Erscheinungsdatum
Reihe/Serie UNITEXT for Physics
Zusatzinfo XVII, 255 p. 5 illus.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Geometrie / Topologie
Naturwissenschaften Physik / Astronomie Allgemeines / Lexika
Naturwissenschaften Physik / Astronomie Theoretische Physik
Schlagworte algebraic topology • Baire's theorem • Banach fixed-point theorem • Banach spaces • Cauchy-Schwarz inequality • Closed graph theorem • Fixed-point techniques • Fredholm equation • Functional Analysis • Functional analysis and transforms • Hahn-Banach theorem • Hilbert spaces • Linear Spaces • Mathematical methods in physics • Mathematical Physics • Metric Spaces • normed spaces • Open mapping theorem • Physics and Astronomy • Semimetric spaces • Semi-normed space • Topological Groups • Topological Spaces • Uniform spaces • vector spaces • Volterra equation
ISBN-10 3-319-35351-9 / 3319353519
ISBN-13 978-3-319-35351-7 / 9783319353517
Zustand Neuware
Haben Sie eine Frage zum Produkt?
Mehr entdecken
aus dem Bereich

von Tilo Arens; Frank Hettlich; Christian Karpfinger …

Buch | Hardcover (2022)
Springer Spektrum (Verlag)
79,99