In complex analysis, the Hardy spaces (or Hardy classes) Hp are certain spaces of holomorphic functions on the unit disk or upper half plane. They were introduced by Frigyes Riesz , who named them after G. H. Hardy, because of the paper . In real analysis Hardy spaces are certain spaces of distributions on the real line, which are (in the sense of distributions) boundary values of the holomorphic functions of the complex Hardy spaces, and are related to the Lp spaces of functional analysis. For 1 ≤ p
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Functions in Hardy spaces on multiply-connected domains in the plane are given an explicit characterization in terms of a boundary condition inspired by the two-dimensional Ising model. The key underlying property is the positivity of a certain operator constructed inductively on the number of components of the boundary.
The aim of the course is to apply the theory of martingales in the context of mathematical finance. The course provides a detailed study of the mathematical ideas that are used in modern financial mathematics. Moreover, the concepts of complete and incomplete markets are discussed.
Calcul différentiel et intégral: Eléments d'analyse vectorielle, intégration par partie, intégrale curviligne, intégrale de surface, théorèmes de Stokes, Green, Gauss, fonctions harmoniques;
Eléments d'analyse complexe: fonctions holomorphes ou analytiques, théorème des résidus et applications
In mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional) Euclidean vector spaces to spaces that may be
In mathematics, more specifically in functional analysis, a Banach space (pronounced ˈbanax) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the co
DISPLAYTITLE:Lp spaceIn mathematics, the Lp spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes called Lebesgue