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Uniform constants in Hausdorff-Young inequalities for the Cantor group model of the scattering transform
Uniform constants Hausdorff-Young inequalities Cantor group model scattering transform
2011/1/21
Analogues of Hausdorff-Young inequalities for the Dirac scattering transform (a.k.a. SU(1, 1) nonlinear Fourier transform) were first established by Christ and Kiselev [1],[2]. Later Muscalu, Tao, and...
We prove that the analogue for the Hilbert transform of a classical weighted inequality by Fefferman and Stein for the Hardy Littlewood maximal operator does not hold. This is a sequel to paper arXiv:...
A proof of the Trisecant Identity through the Fourier-Mukai transform
the Trisecant Identity the Fourier-Mukai transform
2010/11/15
Using the technique of the Fourier-Mukai transform we give an explicit set of generators of the ideal defining an algebraic curve as a subscheme of its Jacobian. Essentially, these ideals are generate...
A remark on primitive cycles and the Radon transform
primitive cycles the Radon transform
2010/11/17
We show that the use of Brylinski's Radon transform elucidates some points of the Green-Griffiths approach to the Hodge conjecture.
Local uniqueness for the Dirichlet-to-Neumann map via the two-plane transform
Dirichlet-to-Neumann map via two-plane transform
2010/10/29
We consider the Dirichlet-to-Neumann map associated to the Schr\"odinger equation with a potential in a bounded Lipschitz domain in three or more dimensions. We show that the integral of the potentia...
The Bianchi-Darboux transform of L-isothermic surfaces
The Bianchi-Darboux transform L-isothermic surfaces
2010/10/29
We study an analogue of the classical Bianchi-Darboux transformation for L-isothermic surfaces in Laguerre geometry, the Bianchi-Darboux transformation. We show how to construct the Bianchi-Darboux tr...
Gravitational Solitons and Monodromy Transform Approach to Solution of Integrable Reductions of Einstein Equations
Gravitational Solitons Monodromy Transform Solution
2010/11/2
In this paper the well known Belinskii and Zakharov soliton generating transformations of the solution space of vacuum Einstein equations with two-dimensional Abelian groups of isometries are consider...