Complements of the theory of functions of a complex variable. Logarithmic indicator and Lagrange’s formula. Mittag-Leffler theorem and Sommerfeld-Watson expansion. Infinite products and Weierstrass expansions. Asymptotic expansions. Laplace method and saddle point techniques. Ordinary differential equations. Green's functions. Sturm-Liouville problems. Fourier and Laplace transforms. Gamma, Beta and Zeta functions. Hypergeometric functions. Bessel functions. Elliptic functions. Partial differential equations. Fundamental solutions. Boundary value problems. Distributions and Their Applications to Differential Equations. Linear operators on Hilbert spaces. Riesz's theorem. Spectral theory. Examples of operators in elle2, of differential operators and of integral operators. Null vectors and the theorem of alternative.
Co-teaching: Dott. Guagnelli Marco