Introduction to Hilbert Spaces with Applications, Second Edition

The Second Edition Of This Successful Text Offers A Systematic Exposition Of The Basic Ideas And Results Of Hilbert Space Theory And Functional Analysis. It Includes A Simple Introduction To The Lebesgue Integral And A New Chapter On Wavelets. The Book Provides The Reader With Revised Examples And Updated Diverse Applications To Differential And Integral Equations With Clear Explanations Of These Methods As Applied To Optimization, Variational And Control Problems, And Problems In Approximation Theory, Nonlinear Instability, And Bifurcation.--jacket. Pt. 1. Theory. Ch. 1. Normed Vector Spaces. Ch. 2. The Lebesgue Integral. Ch. 3. Hilbert Spaces And Orthonormal Systems. Ch. 4. Linear Operators On Hilbert Spaces -- Pt. 2. Applications. Ch. 5. Applications To Integral And Differential Equations. Ch. 6. Generalized Functions And Partial Differential Equations. Ch. 7. Mathematical Foundations Of Quantum Mechanics. Ch. 8. Wavelets. Ch. 9. Optimization Problems And Other Miscellaneous Applications. Lokenath Debnath, Piotr Mikusiński. Includes Bibliographical References And Index.