Functional Analysis, Spectral Theory, and Applications (Graduate Texts in Mathematics, 276) by Manfred Einsiedler (PDF)

Description

This textbook provides a careful treatment of functional analysis and some of its applications in analysis, number theory, and ergodic theory.In addition to discussing core material in functional analysis, the authors cover more recent and advanced topics, including Weyl’s law for eigenfunctions of the Laplace operator, amenability and property (T), the measurable functional calculus, spectral theory for unbounded operators, and an account of Tao’s approach to the prime number theorem using Banach algebras. The book further contains numerous examples and exercises, making it suitable for both lecture courses and self-study.Functional Analysis, Spectral Theory, and Applications is aimed at postgraduate and advanced undergraduate students with some background in analysis and algebra, but will also appeal to everyone with an interest in seeing how functional analysis can be applied to other parts of mathematics.

User’s Reviews

Editorial Reviews: Review “All chapters end with a very useful list of additional topics and suggestions for further reading. The book also contains an appendix on set theory and topology, another one on measure theory … . The book is carefully written and provides an interesting introduction to functional analysis with a wealth of both classical and more recent applications.” (Michael M. Neumann, Mathematical Reviews, July, 2018)“This is an attractive new textbook in functional analysis, aimed at … graduate students. … the large amount of material covered in this book … as well its overall readability, makes it useful as a reference as well as a potential graduate textbook. If you like functional analysis, teach it, or use it in your work, this book certainly merits a careful look.” (Mark Hunacek, MAA Reviews, January, 2018).“The present book is different from the usual textbooks on functional analysis: it does not only cover the basic material, but also a number of advanced topics which cannot be found in many other books on the subject. … The text is suitable for self-study as well as for the preparation of lectures and seminars. … this is a highly recommendable book for students and researchers alike who are interested in functional analysis and its broad applications.” (Jan-David Hardtke, zbMATH 1387.46001, 2018) From the Back Cover This textbook provides a careful treatment of functional analysis and some of its applications in analysis, number theory, and ergodic theory.In addition to discussing core material in functional analysis, the authors cover more recent and advanced topics, including Weyl’s law for eigenfunctions of the Laplace operator, amenability and property (T), the measurable functional calculus, spectral theory for unbounded operators, and an account of Tao’s approach to the prime number theorem using Banach algebras. The book further contains numerous examples and exercises, making it suitable for both lecture courses and self-study.Functional Analysis, Spectral Theory, and Applications is aimed at postgraduate and advanced undergraduate students with some background in analysis and algebra, but will also appeal to everyone with an interest in seeing how functional analysis can be applied to other parts of mathematics. About the Author Manfred Einsiedler studied mathematics at the University of Vienna and has been a Professor at the ETH Zürich since 2009. He was an invited speaker at the 2008 European Mathematical Congress in Amsterdam and the 2010 International Congress of Mathematicians in Hyderabad. His primary research area is ergodic theory with connections to number theory. In cooperation with Lindenstrauss and Katok, Einsiedler made significant progress towards the Littlewood conjecture. Thomas Ward studied mathematics at the University of Warwick and is Deputy Vice-Chancellor for student education at the University of Leeds. He works in ergodic theory and number theory, and has written several monographs, including Heights of Polynomials and Entropy in Algebraic Dynamics with Graham Everest and Ergodic Theory: with a view towards Number Theory with Manfred Einsiedler. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Nice book

⭐This is an awesome and very fresh book in Functional Analysis, it covers both the usual material and also a large number of advanced topics and applications in a very lucid manner. This book is delightful, and it has a special charm due to the care that the authors have put in writing it. This book really deserves a careful look and reading. I give it 4.5/5I have no complaint with the contents of the book itself, but rather with the print quality. The book is very sturdy and the paper is good, but the print quality is not (which is quite weird and a little annoying, because everything else is very good)

⭐Good book. Maybe too much author oriented if that is a flaw. Anyway a good Functional Analysis book to stand besides Lax, Rudin, Conway, but not at the level of Riesz/Nagy or Yosida.

⭐El libro como tal es sumamente bueno, es una gran alternativa para estudiar Análisis Funcional con un enfoque muy bonito y fresco (tiene muchos temas avanzados que no suelen darse en los cursos o mayoría de libros). Aunque es un libro avanzado para principiantes, tampoco es extremadamente especializado, así que puede servir y gustar tanto a gente ambiciosa que va iniciando y quiere ver el tema desde otra perspectiva, como a los que ya saben algo (o mucho) del tema en general. Algo que me gustó mucho es que es muy claro, consistente, tiene muchos ejercicios interesantes y usa buena notación, se nota el profesionalismo y el gusto que tienen los autores por este apasionante tema. Al libro le doy un 4.5/5, es uno de esos títulos que tienen algo para todo el mundo, y le sacan una sonrisa a cualquier apasionado de las matemáticas y del análisis en particular.Ahora, en cuanto a lo que recibí: pirita que quiere parecer oro. De entrada, el empastado era malo y muy rígido, pues aunque se podía abrir lo suficiente, con el grosor del libro (más de 600 páginas) a la larga las hojas de soporte que van pegadas a la pasta se comienzan a vencer. Con un libro tan grueso es obligatorio ir cosido y pegado, este solamente estaba pegado con un pegamento bastante cuestionable; además, la impresión era borrosa (como una impresora casera, y en algunas partes peor), los caracteres no eran suficientemente nítidos como uno esperaría en un título de una editorial científica de prestigio que maneja precios que moran el terreno de los miles de pesos.

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