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I am a Ph.D. student in economics and I plan to study functional analysis by myself either this winter or the next summer. I am currently looking for a textbook, and since I am studying it by myself, I would like the textbook to have complete solutions to all or at least many (say, all odd numbered) problems. I have taken a graduate real variables sequence, but have never studied functional analysis before. So preferably, this doesn't have to be a very advanced text.

Is there any suggestions? Actually it doesn't have to be a book; well written online notes or course websites with complete solutions to exercise/homework problems would be great as well.

Of course I will attempt the problems by my own effort first, but since I won't have anyone to discuss with, I hope that I can have some last resort whenever I cannot figure out a problem.

Thank you very much!

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  • $\begingroup$ Why do you need functional analysis if you are doing a PhD in economics? $\endgroup$ – Lost1 Nov 11 '13 at 0:57
  • $\begingroup$ possible duplicate of Good book for self study of functional analysis; see also problem books in functional analysis. $\endgroup$ – Nate Eldredge Nov 11 '13 at 1:00
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    $\begingroup$ @Lost1: Mathematical finance? $\endgroup$ – Nate Eldredge Nov 11 '13 at 1:01
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    $\begingroup$ I want to apologize for the math folks' ignorance about econ. Stokey and Lucas is basically a book on analysis, at the undergraduate level. Functional analysis is mostly not explicit (until the very end and even then it's bare bones) but it is informed by the functional analytic point of view throughout. Well, all of basic analysis (real, complex, harmonic) can be viewed in the FA context but it's nice to get some macro along with it. Try that first. $\endgroup$ – Michael Nov 11 '13 at 2:32
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    $\begingroup$ @FangJing: The question on problem books in functional analysis specifically asks for books with solutions, and the books suggested do have them. $\endgroup$ – Nate Eldredge Nov 12 '13 at 1:40
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Erwin Kreyszig, Introductory Functional Analysis with Applications

  1. This book has solutions to all odd numbered questions at the back, so you can attempt to work on the problems first, and look at the solutions only when you have to. (This is better than having hints following the problem statements immediately so as to distract you from first concentrating on solving the problems by yourself.)
  2. The exercise problems are attached to each section, as opposed to putting a chapter's worth of problems only at the very end of a chapter. Therefore one could work on the exercises right after finish reading a section, when the memory is still fresh; and the problem solving is broken down into pieces so as not to overtire yourself.
  3. This is a rather elementary book on functional analysis, with minimal prerequisites.

Over all, a great book well suited for my needs.

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    $\begingroup$ I haven't read this book, but to vouch for his writing style, I found his Introduction to differential geometry and Riemannian geometry helpful. $\endgroup$ – rschwieb Dec 30 '13 at 17:41
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Try Functional analysis, sobolev spaces and PDE's by H. Brezis. It's got a rather large collection of problems, with solutions. P.R. Halmos' "A Hilbert space problem book" is another very nice reference.

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I have not taken this course, but it may be something to look into.

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