## Lecture Notes

### Functional Analysis/Fourier Analysis

#### Lecture Notes

#### Functional Analysis

#### Fourier Analysis

#### Problem Sets

#### Functional Analysis

#### Fourier Analysis

#### References and Further Reading

Click on linked topics to view lecture notes.

Metric Spaces

\(\ell^p\) and \(L^p\) as Metric Spaces

Basic (Metric) Topology

Convergence, Cauchy Sequence, Completeness

Completion of Metric Spaces

Normed Spaces and Banach Spaces

Further Properties of Normed Spaces

Linear Operators

Bounded and Continuous Operators

Linear Functionals

Fourier Series

Spectrum

Bessel's Inequality

A Convergence Theorem for Fourier Series

Click on the following links topics for problems.

Problem Set 1. Metric Spaces

Problem Set 2. Basic Topology

Problem Set 3. Convergence, Cauchy Sequence, Completeness

Problem Set 4. Normed Spaces and Banach Spaces, Further Properties of Normed Spaces

Problem Set 5. Linear Operators, Bounded and Continuous Operators

Problem Set 6. Linear Functionals

Gerald B. Folland, Fourier Analysis and Its Applications, Pure and Applied Undergraduate Texts, American Mathematical Society, 2009

Sigurdur Helgason, Topics in Harmonic Analysis on Homogeneous Space, BirkhĂ¤user

Erwin Kreyszig, Introductory Functional Analysis with Applications, 1st Edition, Wiley, 1989

Michael Reed and Barry Simon, Methods of Mathematical Physics I: Functional Analysis, Revised and Enlarged Edition, Academic Press, 1980

Michael Reed and Barry Simon, Methods of Mathematical Physics II: Fourier Analysis, Self-Adjointness, Academic Press, 1972

Michael Reed and Barry Simon, Methods of Mathematical Physics III: Scattering Theory, Academic Press, 1972

Michael Reed and Barry Simon, Methods of Mathematical Physics IV: Analysis of Operators, Academic Press, 1978

H. L. Royden, Real Analysis, Second Edition, The Macmillan Company

Peter Szekeres, A Course in Modern Mathematical Physics, Groups, Hilbert Space and Differential Geometry, Cambridge University Press, 2004