Functional Analysis for the Applied Sciences

• Main Author: Moroşanu, Gheorghe (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Universitext,
• Subjects: Functional analysis.; Partial differential equations.; Differential equations.; Integral equations.; Algebras, Linear.; Functional Analysis.; Partial Differential Equations.; Ordinary Differential Equations.; Integral Equations.; Linear Algebra.

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 equat...

Table of Contents:

• 1. Introduction
• 2. Metric Spaces
• 3. The Lebesgue Integral and Lp 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.