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Multivariate numerical differentiation
International audience -
The Formal Theory of Birth-and-Death Processes, Lattice Path Combinatorics, a...
Classic works of Karlin-McGregor and Jones-Magnus have established a general correspondence between continuous-time birth-and-death processes and continued fractions... -
Weighted $H^2$ Approximation of Transfer Functions
The aim of this work is to generalize to the case of weighted $L^2$ spaces some results about $L^2$ approximation by analytic and rational functions which are useful... -
Disconjugacy, regularity of multi-indexed rationally-extended potentials, and...
The power of the disconjugacy properties of second-order differential equations of Schrödinger type to check the regularity of rationally-extended quantum potentials... -
Mixed correlation function and spectral curve for the 2-matrix model
latex, 1 figure, 55 pages -
New rational extensions of solvable potentials with finite bound state spectrum
Using the disconjugacy properties of the Schrödinger equation, it is possible to develop a new type of generalized SUSY QM partnership which allows to generate new... -
Zero distributions via orthogonality
We develop a new method to prove asymptotic zero distribution for different kinds of orthogonal polynomials. The method directly uses the orthogonality relations. We... -
Landau-Kolmogorov inequalities in Sobolev spaces
This thesis is devoted to Landau-Kolmogorov type inequalities in L2 norm. The measures which are used, are the Hermite, the Laguerre-Sonin and the Jacobi ones. These... -
Geometrical aspects of random matrices
This thesis deals with the geometric and integrable aspects associated with random matrix models. Its purpose is to provide various applications of random matrix... -
Orthogonal polynomials and diffusions operators
We want to describe the triplets (\Omega, (g), \mu) where (g) is the (co)metric associated to some symmetric second order differential operator L defined on the domain... -
PLS: a new statistical insight through the prism of orthogonal polynomials
Partial Least Square (PLS) is a dimension reduction method used to remove multicollinearities in a regression model. However contrary to Principal Components Analysis...
