| This text introduces the basic elements of Linear Functional Analysis: Banach spaces and linear operators; spectrum and resolvent; Baire Theorem and its consequences; Hahn-Banach Theorem; dual spaces and weak convergence. Hilbert spaces: Theorem of projections and abstract Fourier expansions (elements of orthogonal polynomials and Bessel functions are presented) Riesz Theorem and adjoint operators; compact operators. The first elements of distributions and Fourier transform of tempered distributions. |
