1- Orthogonal polynomials.
a) Standard orthogonality. Analytic properties of orthogonal polynomials on the real line. Zeros and asymptotic properties
of orthogonal polynomials. Spectral properties of differential operators and integrable systems.
b) Ortogonality with respect to a measure supported on the unit circle. Szegö's theory and its generalizations.
Applications in signal theory and linear prediction
c) Other models of orthogonality: Sobolev, matrix, multiple, multivariate.
2- Rational approximation.
a) Padé approximation. Applications.
b) Hermite-Padé approximation. Applications.
c) Fourier-Padé approximation. Applications.
3- Geométrica theory of functions.
a) Poincaré metrics and elementary properties.
b) Liouville type theorems.
c) Bounds on the increase of holomorphic functions. Applications.