Iterated integrals of orthogonal polynomials and applications

Résumé

The purpose of this doctoral thesis is on the one hand the study of algebraic and analytical properties of families of polynomials obtained by iterated integration until a fixed order m, of families of orthogonal polynomials with respect to a measure supported in the real line or an arc of the unit circle. On the other hand, create an algorithm for edge detection on gray scale digital images using linear combinations of two dimensional Krawtchouk polynomials.