Faculty of Science

Objectives

To introduce students to the fundamental tools of spectral analysis of operators and the link to solution of differential equations.

Contents

Elements of spectral theory in Banach spaces; Spectral decomposition of self-adjoint and compact normal operators in a separable Hilbert space; Spectral decomposition of bounded and unbounded self-adjoint operators; Hilbert sum and integral associated with the spectral decomposition of self-adjoint operators in a separable Hilbert space; Polynomial expansion of functions (Legendre, Laguerre, Harmonic, Chebyschev, Bessel, etc.); The curl, gradient and divergence operators.