Introduction to Hilbert Spaces with Applications


  • Lokenath Debnath, University of Central Florida, Orlando, U.S.A.
  • Piotr Mikusinski, University of Central Florida, Orlando, U.S.A.

Building on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, 3E, offers an overview of the basic ideas and results of Hilbert space theory and functional analysis. It acquaints students with the Lebesgue integral, and includes an enhanced presentation of results and proofs. Students and researchers will benefit from the wealth of revised examples in new, diverse applications as they apply to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation. The text also includes a popular chapter on wavelets that has been completely updated. Students and researchers agree that this is the definitive text on Hilbert Space theory.
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2-semester course on Functional Analysis or Hilbert space course for junior-senior-grad math students, Also researchers and others interested in math theory.


Book information

  • Published: September 2005
  • ISBN: 978-0-12-208438-6


"...this is a very useful and good book and it can find a place in the library of anybody interested in functional analysis, particularly Hilbert Spaces and their applications." -MAA REVIEWS

Table of Contents

CHAPTER 1 Normed Vector SpacesCHAPTER 2 The Lebesgue IntegralCHAPTER 3 Hilbert Spaces and Orthonormal SystemsCHAPTER 4 Linear Operators on Hilbert SpacesCHAPTER 5 Applications to Integral and Differential EquationsCHAPTER 6 Generalized Functions and Partial Differential EquationsCHAPTER 7 Mathematical Foundations of Quantum MechanicsCHAPTER 8 Wavelets and Wavelet TransformsCHAPTER 9 Optimization Problems and Other Miscellaneous Applications