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
ℓp and Lp 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, Birkhäuser
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