Search results for "Infinite dimension"

showing 2 items of 2 documents

Convexities and optimal transport problems on the Wiener space

2013

The aim of this PhD is to study the optimal transportation theory in some abstract Wiener space. You can find the results in four main parts and they are aboutThe convexity of the relative entropy. We will extend the well known results in finite dimension to the Wiener space, endowed with the uniform norm. To be precise the relative entropy is (at least weakly) geodesically 1-convex in the sense of the optimal transportation in the Wiener space.The measures with logarithmic concave density. The first important result consists in showing that the Harnack inequality holds for the semi-group induced by such a measure in the Wiener space. The second one provides us a finite dimensional and dime…

Convexité[ MATH.MATH-GM ] Mathematics [math]/General Mathematics [math.GM][MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Monge-Ampère equationConvexityMonge problem[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM]Dimension infinieTransport optimalLogarithmic concave measureWiener spaceEspace de WienerOptimal transportÉquation de Monge-AmpèreMesure logarithmiquement concaveProblème de MongeInfinite dimension
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Bloch functions on the unit ball of an infinite dimensional Hilbert space

2015

The Bloch space has been studied on the open unit disk of C and some ho- mogeneous domains of C n . We dene Bloch functions on the open unit ball of a Hilbert space E and prove that the corresponding space B(BE) is invariant under composition with the automorphisms of the ball, leading to a norm that- modulo the constant functions - is automorphism invariant as well. All bounded analytic functions on BE are also Bloch functions. ones, resulting the fact that if for a given n; the restrictions of the function to the n-dimensional subspaces have their Bloch norms uniformly bounded, then the function is a Bloch one and conversely. We also introduce an equivalent norm forB(BE) obtained by repla…

Unit sphereBloch spaceBloch sphereBounded functionMathematical analysisBloch functionUniform boundednessBall (mathematics)Infinite dimensional holomorphyAnalysisMathematicsAnalytic functionBloch wave
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