Functional Analysis for the Applied Sciences

1. Front Matter

   Pages i-xii

   PDF

2. Introduction

   • Gheorghe Moroşanu

   Pages 1-30

3. Metric Spaces

   • Gheorghe Moroşanu

   Pages 31-63

4. The Lebesgue Integral and L^p Spaces

   • Gheorghe Moroşanu

   Pages 65-88

5. Continuous Linear Operators and Functionals

   • Gheorghe Moroşanu

   Pages 89-106

6. Distributions, Sobolev Spaces

   • Gheorghe Moroşanu

   Pages 107-164

7. Hilbert Spaces

   • Gheorghe Moroşanu

   Pages 165-199

8. Adjoint, Symmetric, and Self-adjoint Linear Operators

   • Gheorghe Moroşanu

   Pages 201-216

9. Eigenvalues and Eigenvectors

   • Gheorghe Moroşanu

   Pages 217-242

10. Semigroups of Linear Operators

    • Gheorghe Moroşanu

    Pages 243-296

11. Solving Linear Evolution Equations by the Fourier Method

    • Gheorghe Moroşanu

    Pages 297-313

12. Integral Equations

    • Gheorghe Moroşanu

    Pages 315-339

13. Answers to Exercises

    • Gheorghe Moroşanu

    Pages 341-427

14. Back Matter

    Pages 429-432

    PDF

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.

• text functional analysis
• Lebesque integral
• continuous linear operator
• Lp spaces
• Sobolev spaces
• Hilbert spaces
• self-adjoint linear operator
• symmetric linear operator
• adjoint linear operator
• semigroups linear operators
• functional analysis applied math
• functional analysis physics
• functional analysis exercise
• partial differential equations
• ordinary differential equations

“‘The book is addressed to graduate students and researchers in applied mathematics and neighboring fields of science’. … the book gives a comprehensive, well-organized and readable introduction to functional analysis with interesting applications in various neighboring fields, always providing full proofs and many valuable exercises.” (Wolfgang Lusky, Mathematical Reviews, March, 2021)

• Romanian Academy of Sciences, Bucharest, Romania, Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

  Gheorghe Moroşanu

Gheorghe Moroşanu is a professor of mathematics who currently holds affiliations with the Central European University, Babeş-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 Moroşanu’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 Moroşanu holds honorary doctorates of the University of Craiova and Ovidius University, Constanta. Recently, he has received the title of Professor Honoris Causa from the Babeş-Bolyai University.

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