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Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space II

Viorel Barbu, Giuseppe Da Prato, Luciano Tubaro (2011)

Annales de l'I.H.P. Probabilités et statistiques

This work is concerned with the existence and regularity of solutions to the Neumann problem associated with a Ornstein–Uhlenbeck operator on a bounded and smooth convex set K of a Hilbert space H. This problem is related to the reflection problem associated with a stochastic differential equation in K.

Kronecker modules and reductions of a pair of bilinear forms

Giovanni Falcone, M. Alessandra Vaccaro (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

We give a short overview on the subject of canonical reduction of a pair of bilinear forms, each being symmetric or alternating, making use of the classification of pairs of linear mappings between vector spaces given by J. Dieudonné.

La controverse de 1874 entre Camille Jordan et Leopold Kronecker

Frédéric Brechenmacher (2007)

Revue d'histoire des mathématiques

Une vive querelle oppose en 1874 Camille Jordan et Leopold Kronecker sur l’organisation de la théorie des formes bilinéaires, considérée comme permettant un traitement « général » et « homogène » de nombreuses questions développées dans des cadres théoriques variés au xixe siècle et dont le problème principal est reconnu comme susceptible d’être résolu par deux théorèmes énoncés indépendamment par Jordan et Weierstrass. Cette controverse, suscitée par la rencontre de deux théorèmes que nous considérerions...

Large structures made of nowhere L q functions

Szymon Głąb, Pedro L. Kaufmann, Leonardo Pellegrini (2014)

Studia Mathematica

We say that a real-valued function f defined on a positive Borel measure space (X,μ) is nowhere q-integrable if, for each nonvoid open subset U of X, the restriction f | U is not in L q ( U ) . When (X,μ) has some natural properties, we show that certain sets of functions defined in X which are p-integrable for some p’s but nowhere q-integrable for some other q’s (0 < p,q < ∞) admit a variety of large linear and algebraic structures within them. The presented results answer a question of Bernal-González,...

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