- Tapa dura: 418 páginas
- Editor: Academic Press; Edición: REV AND ENL (1 de enero de 1981)
- Colección: Methods of Modern Mathematical Physics
- Idioma: Inglés
- ISBN-10: 0125850506
- ISBN-13: 978-0125850506
- Valoración media de los clientes: Sé el primero en opinar sobre este producto
- Clasificación en los más vendidos de Amazon: nº510.762 en Libros en idiomas extranjeros (Ver el Top 100 en Libros en idiomas extranjeros)
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I: Functional Analysis: Volume 1: vol 1 (Methods of Modern Mathematical Physics) (Inglés) Tapa dura – 1 ene 1981
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This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modern physics, and partial differential equations.
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However, the actual book that I received felt almost like photocopy quality and was difficult to read. The whole point of purchasing such an expensive text is to have it in your hands without the strain of staring at a computer screen. Elsevier did a downright crappy job with the new version (not the old maroon one).
However, do not expect ready-brew formulae and cookbook recipes: this book gets his job done at least as well as Rudin, Yosida and Riesz-Sz.Nagy, just to mention the classics. Most theorems are rigorously proved, and although the book becomes more and more biased towards mathematical physics (i.e., methods for proving self-adjointness, analysis of spectra and scattering theory, as stated in the section "Three Mathematical Problems in Quantum Mechanics". These methods occupy most of the three remaining volumes) as it proceeds - this bias becomes the true reason of being for the last two volumes - this particular volume has precisely the most useful stuff: metric, Banach, topological, locally convex, and Hilbert spaces, bounded and unbounded operators. A supplement extracted from the second volume with the basics of Fourier transforms makes it self-contained as a monograph.
However, the best things, that make this book nearly unbeatable, are the several wisely chosen examples and counterexamples, the notes at the end of each chapter and the wonderful - and useful - exercises. Many working mathematicians I know use this book seriously in their research and their courses in Functional Analysis - a fact that cannot be underestimated and will hardly be equaled by any book on mathematical physics.
If you work on (axiomatic) quantum field theory you may also want to keep an eye on the second volume of the set, "Fourier Analysis, Self-adjointness", which is a bit more specialized but just as wonderful.