MATH 510 Hilbert Space Theory with Applications

The Lebesque integral. Hilbert spaces. Linear operators. Fredholm integral equation. Voltera integral equation, Applications to ordinary differential equations. Sturm-Liouville systems. Inverse differential operators and Green’s functions. Application of Fourier transform to ordinary differential and integral equations. Generalized functions. Fundamental solutions and Green’s function for partial differential equations. Week solutions of elliptic boundary value problems, Applications of Fourier transform to partial differential equations. Miscellaneous applications to equations of mathematical physics.