Functional Analysis by M. Reed and B. Simon, parts I, II. Operator Theory (part 4) by B. Simon, AMS 2016.
Topics covered will include: review of Hilbert spaces and Operators.
Spectral Theorem for bounded and unbounded Operators.
Compact Operators and Introduction to Spectral Theory: Fredholm Theorem, Weyl, Resolvent Estimates.
Duality, Distributions and Fourier transforms.
All topics will include examples from Partial Differential equations, Mathematical-Physics and Differential Geometry.