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6 papers · 1 filter
Matrix differential equations and scalar polynomials satisfying higher order recursions
Antonio J. Duran, F. Alberto Grünbaum
We show that any scalar differential operator with a family of polyno- mials as its common eigenfunctions leads canonically to a matrix differen- tial operator with the same proper…
The power law for the Buffon needle probability of the four-corner Cantor set
Fedor Nazarov, Yuval Peres, Alexander Volberg
Let be the -th generation in the construction of the middle-half Cantor set. The Cartesian square of consists of squares of side-length . The cha…
The Rahman Polynomials Are Bispectral
F. Alberto Grünbaum
In a very recent paper, M. Rahman introduced a remarkable family of polynomials in two variables as the eigenfunctions of the transition matrix for a nontrivial Markov chain due to…
Mixed norm estimates for certain generalized Radon transforms
Michael Christ, M. Burak Erdogan
In this paper we investigate the mapping properties in Lebesgue-type spaces of certain generalized Radon transforms defined by integration over curves.
Finite bounds for Holder-Brascamp-Lieb multilinear inequalities
Jonathan Bennett, Anthony Carbery, Michael Christ +1
A criterion is established for the validity of multilinear inequalities of a class considered by Brascamp and Lieb, generalizing well-known inequalities of Holder, Young, and Loomi…
On multilinear oscillatory integrals, nonsingular and singular
Michael Christ, Xiaochun Li, Terence Tao +1
Basic questions concerning nonsingular multilinear operators with oscillatory factors are posed and partially answered. Lebesgue space norm inequalities are established for multili…