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Littelmann path model for geometric crystals, Whittaker functions on Lie grou...
Generally speaking, this thesis focuses on the interplay between the representations of Lie groups and probability theory. It subdivides into essentially three parts.... -
Positive stable densities and the bell-shape
We show that positive stable densities are bell-shaped, that is their n-th derivatives vanish exactly n times on (0,+oo) and have an alternating sign sequence. This... -
Total positivity of a Cauchy kernel
We study the total positivity of the kernel $1/(x^2 + 2 \cos(\pi\a)xy +y^2).$ The case of infinite order is characterized by an application of Schoenberg's theorem. We... -
Polynomial splines as examples of Chebyshevian splines
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On a new criterion to decide whether a spline space can be used for design
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Shape constraints and optimal bases for C1 Hermite interpolatory subdivision ...
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Chebyshev-Schoenberg operators
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Mixed hyperbolic/trigonometric spaces for design
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Design with L-splines
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On a general new class of quasi Chebyshevian splines
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Optimal bases for C1 Hermite Subdivision Schemes
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