Abstract

Building on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, Third Edition, 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.

• Updated chapter on wavelets
• Improved presentation on results and proof
• Revised examples and updated applications
• Completely updated list of references

"I think this is a superb text for an applied math class (at the upper level undergraduate
or graduate level)! The introduction to Hilbert spaces and other material presented in Chapters 1–4 open the doors to a number of applications as presented in Chapters 5–9.", Robert Gardner, East Tennessee State University.
"This is a unique book which includes both a rigorous development of issues related to Hilbert Spaces, but also gives a wide variety of useful applications..." Joseph M. Powers, University of Notre Dame