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.
Author(s): Gheorghe Moroşanu
Series: Universitext
Edition: 1
Publisher: Springer
Year: 2020
Language: English
Pages: 439
Tags: Lebesgue Integral, Linear Operators, Distributions, Sobolev Spaces, Hilbert Spaces, Semigroups
Front Matter ....Pages i-xii
Introduction (Gheorghe Moroşanu)....Pages 1-30
Metric Spaces (Gheorghe Moroşanu)....Pages 31-63
The Lebesgue Integral and Lp Spaces (Gheorghe Moroşanu)....Pages 65-88
Continuous Linear Operators and Functionals (Gheorghe Moroşanu)....Pages 89-106
Distributions, Sobolev Spaces (Gheorghe Moroşanu)....Pages 107-164
Hilbert Spaces (Gheorghe Moroşanu)....Pages 165-199
Adjoint, Symmetric, and Self-adjoint Linear Operators (Gheorghe Moroşanu)....Pages 201-216
Eigenvalues and Eigenvectors (Gheorghe Moroşanu)....Pages 217-242
Semigroups of Linear Operators (Gheorghe Moroşanu)....Pages 243-296
Solving Linear Evolution Equations by the Fourier Method (Gheorghe Moroşanu)....Pages 297-313
Integral Equations (Gheorghe Moroşanu)....Pages 315-339
Answers to Exercises (Gheorghe Moroşanu)....Pages 341-427
Back Matter ....Pages 429-432
