Functional Analysis and Infinite-Dimensional Geometry. It has a lot of nice exercises, it's less abstract than the usual book and provides a lot of "concrete" theorems. And I'm not sure about it, but I heard there is a spanish translation the original is of course in english.
I'd recommend the Dunford and Schwartz. It's a classic.
Spectral Theory and its Applications. Control of violent behavior through faradic shock: A case study. Towards a cognitive resource limitations model of diminished expression in schizotypy. Progressing from initially ambiguous functional analyses: Three case examples. Differentiation is an example of a functional because it defines a relationship between a function and another function its derivative. The subjects are covered at a good pace with proofs that can be easily understood, but are not devoid of depth. Psychological interventions for psychosis: a meta-analysis of comparative outcome studies.
It's huge -- three volumes. But you don't have to read the whole series cover-to-cover. If you read half of the first volume, you'll learn about as much as reading many other books on functional analysis. Volume 1 alone is big, but it's easy to read for a book on its subject. One of the differences with other books on the subject is that it uses the categorical point of view. The author starts with a very brief introduction to the category theory and uses this language throughout the book.
It's a sort of modern core of FA book, with a sidelines to some physics applications and of historic nature, a terse advertisement of the quantum functional analysis and so on but there is no measure theory, Radon Nikodym theorem etc. Also it gives somewhat broader picture of FA sketching some directions and stating from time to time theorems without proofs 'that every student should know'.
Zimmer's Essential Results of Functional Analysis is a very interesting read, specially if you already know some basic stuff in functional analysis. There is also a German version if you want to improve your German by reading both together. It seems like you may already know the first few chapters, however. I have learnt Functional Analysis from Peter Lax himself. His book is his notes. Exactly the same notes as the ones he handed to us.
Every chapter consists of one two-hours long lecture in a two semester graduate course on Functional Analysis. It is as if you are in a class of Peter Lax! Having said all these, I should add that as an undergraduate student, I had taken two semesters of Functional Analysis which covered a part of Rudin's book. I still use this book sometimes, as some topics are presented in a beautiful way, but I believe that it is far from introductory, as it starts with Topological Vector Spaces, and it takes a while before normed spaces are mentioned.
I second Reed and Simon's methods of mathematical physics. However, if you are interested primarily in the applications of functional analysis to PDE, for the most part a couple of appendices of Evans' book suffice in my opinion. Let me add to this list of suggestions the nice and recent book by J.
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Active 2 years, 4 months ago. Viewed 60k times. If you are interesting in spectral theory, the classic 4 volume treatise by Reed and Simon, modern methods of mathematical physics is definitely recommended. Maybe you could list the most advanced topics in functional analysis and topology that you've covered in class; then we'd all know what it would mean to "go deeper". Then we did some work three days on Banach algebras how to proof a subspace is dense in them.
A credit in the European Union is between 20 and 25 hours of work in class and home. Seeing the historical motivation for the basic concepts was quite enlightening for me. In case you don't know, you can edit your original question using the "edit" button below it. And by the way, the credit system is not uniform through the EU: e.
Salvatore Siciliano. All the more interesting since I think the book is dull as dishwater. Sobolev spaces are horribly shorted, and treated clumsily when they briefly appear. Quasi-completeness is ignored entirely. These are not odd, isolated topics. Certain books, when taken biblically by an advisor for example, can serve to dampen mathematical intuition to a criminal degree.
I'm NOT saying Rudin's book has this property I've found this book a very clear and useful reference recently. I'm not going to ask such a question because it really wouldn't be right to do so Chris Godsil. A really great book And it's clearly designed for students with some familiarity with the concepts,so it may be just what you're looking for, Dan. Pieter Naaijkens. Functional Analysis, by F. Riesz and Nagy. Analysis now.
Elementary Functional Analysis by Georgi E. Notes on Functional Analysis by Rajendra Bhatia. Hindustan Book Agency. Functional Analysis by S.
Elementary functional analysis By Barbara D. One thing that I enjoy, at least with their Real Analysis book is that it is not as "clean" as some of the other texts that have been around for so long and therefore forces some extra thinking on the part of the reader. Some might not like this, but as a student it helped me. This was the text for a course at Harvard I took with Barry Simon, who was I think then an undergraduate. Mahdi Majidi-Zolbanin.
Some of the subjects include Hilbert, Lebesgue, Enflo, and von Neumann. For people who are cited, but did not have their biographies included, the years of their life and birth country follow their name e. Sergei Bernstein ; Ukraine. Many times students come to the conclusion that mathematics is a dry subject and even worse a finished product that has not grown in a hundred years.
Saxe does a wonderful job showing how functional analysis developed over the years and how international the body of mathematicians working on it truly is. I wish there were more of these biographies. This is a good book for students to learn functional analysis. It is also one that students will enjoy using and out of which they will get more than just the nuts and bolts of the topics.
Robert W. His research interests are real analysis and topology. He can be reached at Robert. Skip to main content. Search form Search.
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