This advanced graduate textbook presents main results and techniques in Functional Analysis and uses them to explore other areas of mathematics and applications. This textbook, with its friendly exposition, focuses on different problems in physics and other applied sciences and uniquely provides solutions to most of the exercises.This advanced graduate textbook presents main results and techniques in Functional Analysis and uses them to explore other areas of mathematics and applications. Special attention is paid to creating appropriate frameworks towards solving significant problems involving differential and integral equations. Exercises at the end of each chapter help the reader to understand the richness of ideas and methods offered by Functional Analysis. Some of the exercises supplement theoretical material, while others relate to the real world. This textbook, with its friendly exposition, focuses on different problems in physics and other applied sciences and uniquely provides solutions to most of the exercises. The text is aimed toward graduate students and researchers in applied mathematics, physics, and neighboring fields of science. 1. Introduction.- 2. Metric Spaces.- 3. The Lebesgue Integral and L p Spaces.- 4. Continuous Linear Operators and Functionals.- 5. Distributions, Sobolev Spaces.- 6. Hilbert Spaces.- 7. Adjoint, Symmetric and Self-adjoint Linear Operators.- 8. Eigenvalues and Eigenvectors.- 9. Semigroups of Linear Operators.- 10. Solving Linear Evolution Equations by the Fourier Method.- 11. Integral Equations.- 12. Answers to Exercises.- Bibliography.
Gheorghe Morosanu is a professor of mathematics who currently holds affiliations with the Central European University, Babes-Bolyai University, and the Romanian Academy of Sciences. Previously, he held positions at the University of Stuttgart and the Alexandru Ioan Cuza University (his Alma Mater). Professor Morosanu's main research interests include differential equations, calculus of variations, fluid mechanics, singular perturbation theory, and various topics in applied mathematics. He is the author or co-author of a great number of research articles and fifteen books (monographs and textbooks). In 1983 he was awarded the Gheorghe Lazar Prize of the Romanian Academy in recognition of his outstanding contributions to the theory of hyperbolic partial differential equations. Additionally, Gheorghe Morosanu holds honorary doctorates of the University of Craiova and Ovidius University, Constanta. Recently, he has received the title of Professor Honoris Causa from the Babes-Bolyai University.
