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Applied Functional Analysis

MATH 725 Applied Functional Analysis

Introduction

Modern Applied Mathematics
Basic Functional Analysis

Linear Operators

Bounded Operators
The Baire Category Theorem
The uniform boundedness principle (Banach-Steinhaus)
The Open Mapping Theorem
Compact Operators

Duality

The Dual-Space
The transpose (adjoint) operator
Examples of dual-spaces
The Hahn-Banach Theorem
The adjoint (transpose) operator

Distributions

Introduction to Distribution Theory
The Space of Test Functions
Distributions as Continuous Linear Functionals
Distributions as Averaging Operators

Jupyter Notebooks

Fourier Series for continuous functions
Deblurring Images

Appendix

Matrix Multiplication
Solving special matrices
Gaussian Elimination

References

Bibliography

Index

By Andreas Buttenschoen.

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