Lecture Notes
Contents: Normed linear spaces. Elements of functional analysis. L_p spaces as examples of Hilbert and Banach spaces. Operators. Dual spaces. Spectral theory. Applications to differential equations. Possible additional topics: K_0 of AF algebras, applications of the current algebra to the moment problem.
Aims and Objectives: Students on this course should learn enough about modern functional analysis to be able to apply the ideas to problems in Fourier Analysis, Ordinary Differential Equations and Partial Differential Equations. Rigorous approaches to convergence of Fourier series and the existence and uniqueness problems for Differential Equations will be developed. Throughout the idea of Functional Analysis as a unifying circle of methods in both Pure and Applied Mathematics will be pursued.
Supplement 1: range and kernel
of adjoint operators
Sheet 1
Sheet 2
Sheet 3
Sheet 4