Conference rusure::math

1513.0. "FYI: Functional analysis Texts outline" by STAR::ABBASI () Tue Oct 29 1991 01:18

    FYI,
    These are some books on Functional Analysis that i've been
    reading from some of them latley , there do not seem to be relatively 
    large numbers of books on the subject. this some idea about what
    i know of:
    
    1) Introductory Functional Analysis with applications by Kreyszig
       john wiley. 
       This has the most Examples , odd problems have solutions in back.
        680 pages, papaer back. cost $36
    
    2) Elements of functional analysis, by Maddox, Cambridge univ. press.
       more rigoures (sp?) than #1, covers basic set theory, Metric and
      topological spaces, linear and linear metric spaces, normed linear
      spaces, Banach algebras, and hilbert spaces, and small section
      on application, less than #1.  229 pages.
    
    3) Finite-dimenstional vector spaces by Paul Halmos (springer-verlag)
       while this is not exaclty a functional analysis text, it covers
       vector spaces, transformations, orthogonality and vector spaces
       analysis.
       190 pages, cost about $35. I did not read a lot from this text,
       but Halmos apparently known to be a very good writer in this field.
       
    4) Engineering analysis, a vector spaces approach, by Schilling and
    Lee. (john willey)
       covers vector spaces, normed vector spaces, inner product spaces,
       linear transformations, finite-dimentional linear transformation,
       linear operators, finite-dimentional linear operators, linear
       differential systems, linear difference systems, and orthogonal
       transformations and amplitude estimation.
    
       333 pages, about $55.
       not well written text, some parts are hard to follow. but covers
       most areas relating to vector spaces, it seems.
    
    5) A course of applied functional analysis by Arthur Wouk, 
       Willey-interscience series of texts in pure and applied math.
       covers metric spaces and fixed points, integration theory, complete
       spaces of integrable functins , separability and compactness, 
       algebraic structure of linear vector spaces, normed spaces and
       continuous operators, theory of appoximate methods and its
       applicatins, minization of quadratic functionals, calculus for
       nonlinear operators, convexity, optimization and control.
    
       just got this book, cant comment on it, it says in introduction
       this:
       this book concerned with these problems:
       1. given a functional equation, find a solution.
       2. given functional defined over a set, find its minimum on the set
       3. given functional equation on a set, find an approx solution in
          some subset
       4. given a functional on set, find its min, subject to constraints
          on a subset
       the above offcourse are important applications of functional analysis
       this is 427 pages, no solutions on back, little examples and
       plenty of theorms and defintions .
    
    6) a Dover book, Banach spaces of analytic functions, by hoffman.
       covers fourie series, analytic and harmonic functions on unit disc,
       space H (for Hardy space) and norms on it, shift operator, Hp spaces
       on half plane, Hp as banach space, H(oo) as banach algebra.
       216 pages,  $7.
    
      
    /nasser
    
    
    

    Reed and Simon's books on the subject are pretty encyclopedic,
    as are Dunford and Schwartz.  Also, books on mathematical physics
    often get into the subject and may be worth looking thru.

    - Jim

    It is really easy to miss books that have a lot of functional analysis
    in them.  A few examples.
    
    "Methods of Mathematical Physics" by Courant and Hilbert.  Although
    Hilbert spaces and Banach spaces are not mentioned, functional analysis
    is a big part of this two volume set.
    
    "Real Analysis and Probability" by Ash.  Lp spaces covered very well.
    
    "Analysis, Manifolds an Physics" by Bruhat, Morette and Bleick.  At
    least half the book one way and another.
    
    "Linear Partial Differential Operators" by L. H�rmander.  Also his four
    volume rewrite.
    
    "Spectral Theory of Operators in Hilbert Space" by K. O. Friedrichs.
    
    "Topology and Modern Analysis" by George F. Simmons (not related to
    me).
    
    And the list goes on and on and on - the words "functional analysis"
    don't have to be in the title.  I could have listed books by Yoshida,
    Berberian, DeVito and others having those words in the title but there
    are so many others as well.  It is a large field with a large
    literature.
    
    Chuck

    
    "Functiona Analysis" by Kosaku Yosida. Springer Verlag.