Functional Analysis by Walter Rudin

Product Description

This classic text is written for graduate courses in functional analysis. This text is used in modern investigations in analysis and applied mathematics. This new edition includes up-to-date presentations of topics as well as more examples and exercises. New topics include Kakutani's fixed point theorem, Lamonosov's invariant subspace theorem, and an ergodic theorem.

This text is part of the Walter Rudin Student Series in Advanced Mathematics.
Product Details
Amazon Sales Rank: #111534 in Books
Published on: 1991-01-01
Number of items: 1
Binding: Hardcover
448 pages
Customer Reviews

As a reference, this is nice, but as a book for first-time learners...
I enjoy perusing Rudin's "Functional Analysis" at this stage in my life. It is fairly nice tome for functional analysis, and its general treatment of topological vector spaces (as opposed to the standard Banach space examples studied in a typical functional analysis class) is now well-received.

However, as a student, I was put off by this book. At times, I found it difficult to tie the theory present to the basic examples which were relevant at the time (such as L^{p} spaces). For a first time learner, I would suggest the book of Kolmogorov and Fomin (which is a Dover book, by the way), and would wait until later for this book.

Outstanding
Hardly can I find words to highlight the goodness of this book. As mentioned by other readers ,it provides elegant, direct and powerfool proofs of the three theorems which constitute the cornserstones of functional analysis (Hanh-Banach, Banach-Steinhaus and Open mapping). These theorems are, in addition, studied in their most general context, namely topological vector spaces.

Specially appealing is its treatment of distributions' theory. It is, as far as I know, the only text which start by defining the rigurous topology on the set of test functions and then obtains the convergence and continuity of functionals (distributions) in terms of this topolgy, which is, indeed, the only way to present and gain insight into these concepts and to reach some results such as completness. In doing otherwise one risk definitions can emerge as artificial and rather arbitrary.

It is, without any doubt, a must have book for those with interest in pure mathematics as well as for those who, eventually, realize that the only way to dominate their area is saling through mathematics.

Modern topics in math.
"Modern analysis" used to be a popular name for the subject of this lovely book. It is as important as ever, but perhaps less "modern". The subject of functional analysis, while fundamental and central in the landscape of mathematics, really started with seminal theorems due to Banach, Hilbert, von Neumann, Herglotz, Hausdorff, Friedrichs, Steinhouse,...and many other of, the perhaps less well known, founding fathers, in Central Europe (at the time), in the period between the two World Wars. In the beginning it generated awe in its ability
to provide elegant proofs of classical theorems that otherwise were thought to be both technical and difficult. The beautiful idea that makes it all clear as daylight: Wiener's theorem on absolutely convergent(AC) Fourier series of 1/f if you can divide, and if f has the AC Fourier series, is a case in point. The new subject gained from there because of its many sucess stories,- in proving new theorems, in unifying old ones, in offering a framework for quantum theory, for dynamical systems, and for partial differential equations. And offering a language that facilitated interdisiplinary work in science! The Journal of Functional Analysis, starting in the 1960ties, broadened the subject, reaching almost all branches of science, and finding functional analytic flavor in theories surprisingly far from the original roots of the subject. The topics in Rudin's book are inspired by harmonic analysis. The later part offers one of the most elegant compact treatment of the theory of operators in Hilbert space, I can think of. Its approach to unbounded operators is lovely.