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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some special cases of the three dimensional Kakeya conjecture and their application to the restriction conjecture
三维Kakeya猜想 特殊情况 限制猜想
2023/5/9
We will discuss two special cases of the three-dimensional Kakeya conjecture: SL_2 Kakeya and a refined Wolff's hairbrush result. As an application of the refined Wolff's hairbrush result, we will dis...
Quantum ergodic restriction for Cauchy data: Interior QUE and restricted QUE
Quantum ergodic restriction Cauchy data Interior QUE restricted QUE Analysis of PDEs
2012/5/24
We prove a quantum ergodic restriction theorem for the Cauchy data of a sequence of quantum ergodic eigenfunctions on a hypersurface $H$ of a Riemannian manifold $(M, g)$. The technique of proof is to...
On the restriction of Zuckerman's derived functor modules A_q(λ) to reductive subgroups
unitary representation Zuckerman’s derived functor module branching law reductive group D-module flag variety
2011/9/6
Abstract: In this paper, we study the restriction of Zuckerman's derived functor (g,K)-modules A_q(\lambda) to g' for symmetric pairs of reductive Lie algebras (g,g'). When the restriction decomposes ...
Extension of Symmetric Spaces and Restriction of Weyl Groups and Invariant Polynomials
Invariant polynomials Extension of symmetric spaces Spherical Fourier transform
2011/1/17
Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant poly-nomial.
Restriction and spectral multiplier theorems on asymptotically conic manifolds
Restriction spectral multiplier theorems asymptotically conic manifolds
2011/2/22
The classical Stein-Tomas restriction theorem is equivalent to the statement that the spectral measure dE() of the square root of the Laplacian on Rn is bounded from Lp(Rn) to Lp′
(Rn) for 1 p 2...
Restriction maps on 1-cohomology of (algebraic) groups
Restriction maps on 1-cohomology of groups
2010/11/11
Our first theorem is a version of the five lemma in a certain situation of pointed sets arising from non-abelian 1-cohomology. For our second, we show that a connected, unipotent algebraic group Q ac...
Toward a Mackey formula for compact restriction of character sheaves
Mackey formula compact restriction character sheaves
2010/11/15
We generalize a result by Cunningham-Salmasian to a Mackey-type formula for the compact restriction of a semisimple perverse sheaf produced by parabolic induction from a character sheaf, under certai...
Restriction estimates for the paraboloid over finite fields
Restriction estimates paraboloid over finite fields
2010/12/7
We prove certain endpoint restriction estimates for the paraboloid over finite fields in
three and higher dimensions. Working in the bilinear setting, we are able to pass from esti-
mates for charac...
Gaussians Rarely Extremize Adjoint Fourier Restriction Inequalities For Paraboloids
Gaussians Rarely Extremize Adjoint Fourier Restriction Inequalities Paraboloids
2011/1/19
Let Pd−1 be the paraboloid in Rd,Pd−1 = {(y′, yd) ∈ Rd−1 × R : yd = |y′|2/2}.Equip Pd−1 with the appropriately dilation-invariant measure on Rd defined by Z Rd f(y′, yd) d(y...
Fourier Restriction Estimates to Mixed Homogeneous Surfaces
Restriction theorems Fourier transform
2010/1/25
Let be real numbers such that and let a mixed homogeneous function. We consider polynomial functions and also functions of the type Let with the Lebesgue induced measure. For and let where d...
The Restriction and the Continuity Properties of Potentials Depending on l-distance
Riesz Potential Non-Isotropic distance
2010/2/26
In this study we establish theorems on the restriction and continuity of the generalized Riesz potentials with the non-isotropic kernels depending on l-distance.