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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Sharp Lp estimates and size of nodal sets of generalized Steklov eigenfunctions
Steklov-eigenfunctions 尖锐 Lp 估计 节点集
2023/4/13
We prove sharp Lp estimates for the Steklov eigenfunctions on compact manifolds with boundary in terms of their L2 norms on the boundary. We prove it by establishing Lp bounds for the harmonic extensi...
Estimates on the amplitude of the first Dirichlet eigenvector in discrete frameworks
fi nite absorbing Markov process fi rst Dirichlet eigenvector path method spectral estimates denumerable absorbing birth and death process entrance boundary.
2015/7/7
Estimates on the amplitude of the first Dirichlet eigenvector in discrete frameworks。
Unbiased Risk Estimates for Singular Value Thresholding and Spectral Estimators
Singular value thresholding Stein’s unbiased risk estimate (SURE) differentiability of eigenvalues and eigenvectors magnetic resonance cardiac imaging
2015/6/17
In an increasing number of applications, it is of interest to recover an approximately low-rank data matrix from noisy observations. This paper develops an unbiased risk estimate—holding in a Gaussian...
L^3 estimates for an algebraic variable coefficient Wolff circular maximal function
L^3 estimates algebraic variable coefficient Wolff circular maximal function
2011/1/17
In 1997, Thomas Wol proved sharp L3 bounds for his circular maximal function, and in 1999, Kolasa and Wol proved certain non-sharp Lp inequalities for a broader class of maximal functions arising fr...
Dispersive estimates and NLS on product manifolds
decay estimates dispersive equations hyperbolic space
2011/1/17
We prove a general dispersive estimate for a Schr¨odinger type equation on a product manifold, under the assumption that the equation restricted to each factor satisfies suitable dispersive estimates....
Asymptotic estimates on the time derivative of entropy on a Riemannian manifold
the time derivative entropy Riemannian manifold
2010/11/23
We consider the entropy of the solution to the heat equation on a Riemannian manifold. When the manifold is compact, we provide two estimates on the rate of change of the entropy in terms of the lower...
Rubio de Francia's extrapolation theory: estimates for the distribution function
Rubio de Francia's extrapolation theory the distribution function
2010/11/15
Let $T$ be an arbitrary operator bounded from $L^{p_0}(w)$ into $L^{p_0, \infty}(w)$ for every weight $w$ in the Muckenhoupt class $A_{p_0}$. It is proved in this article that the distribution functi...
Estimates of the Green function for the fractional Laplacian perturbed by gradient
Estimates of the Green function fractional Laplacian
2010/12/6
The Green function of the fractional Laplacian of the differential order bigger than one and the Green function of its gradient perturba-tions are comparable for bounded smooth multidimensional open s...
Gradient estimates for a simple nonlinear heat equation on manifolds
nonlinear heat equation gradient estimate
2010/11/29
In this paper, we study the gradient estimate for positive solutions to the following nonlinear heat equation problem ut − u = au log u + V u, u > 0 on the compact Riemannian manifold (M, g) of...
Hamilton type estimates for heat equations on manifolds
drifting Laplacian nonlinear heat equation gradient estimate
2010/11/29
In this paper, we study the gradient estimates of Hamilton type for positive solutions to both drifting heat equation and the simple nonlinear heat equation problem ut − u = au log u, u > 0 on ...
Curvature estimates for submanifolds in warped products
Warped product manifolds Omori-Yau maximum principle weak Omori-Yau maximum principle
2010/12/8
We give estimates on the intrinsic and the extrinsic cur-vature of manifolds that are isometrically immersed as cylindrically bounded submanifolds of warped products. We also address extensions of the...
Heat kernel estimates for the $\bar\partial$-Neumann problem on $G$-manifolds
Heat kernel estimates $\bar\partial$-Neumann problem $G$-manifolds
2010/12/13
We prove heat kernel estimates for the ¯@-Neumann Laplacian acting in spaces of differential forms over noncompact manifolds with a Lie group symmetry and compact quotient. We
also relate our ...
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...
Argument Estimates For Certain Analytic Functions Associated With The Convolution Structure
Argument estimate Subordination Univalent function Hadamard product(or convolution) Dziok-Srivastava operator
2010/1/22
The purpose of the present paper is to investigate some argument properties for certain analytic functions in the open unit disk associated with the convolution structure. Some interesting application...