Spectral Theory Of Compact Linear Operators And Applications

This Project primarily falls into the field of Linear Functional Analysis and its Applications to Eigenvalue problems. It concerns the study of Compact Linear Operators (i.e., bounded linear operators which map the closed unit ball onto a relatively compact set) and their spectral analysis applicable to Fourier Analysis and to the solvability of Fredholm Integral Equations, linear elliptic Partial Differential Equations (PDEs) with the Dirichlet boundary condition, Sturm-Liouville problems, and of Optimization problems.