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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...
On the eigenfunctions of the complex Ornstein-Uhlenbeck operators
eigenfunctions complex Ornstein-Uhlenbeck operators
2016/1/25
Starting from the 1-dimensional complex-valued Ornstein-Uhlenbeck process, we present two natural ways to imply the associated eigenfunctions of the 2-dimensional normal Ornstein-Uhlenbeck operators i...
Generalized eigenfunctions and a Borel Theorem on the Sierpinski Gasket
Generalized eigenfunctions Borel Theorem Sierpinski Gasket
2015/12/10
There is a well developed theory (see [5, 9]) of analysis on certain types of fractal sets, of which the Sierpinski Gasket (SG) is the simplest non-trivial example. In this theory the fractals are vie...
Geometrical structure of Laplacian eigenfunctions
Laplace operator eigenfunctions eigenvalues localization
2012/6/25
We review the properties of eigenvalues and eigenfunctions of the Laplace operator in bounded Euclidean domains with Dirichlet, Neumann or Robin boundary condition. We keep the presentation at a level...
Geodesic restrictions of eigenfunctions on arithmetic surfaces
Geodesic restrictions of eigenfunctions arithmetic surfaces Number Theory
2012/4/23
Let X be an arithmetic hyperbolic surface, {\psi} a Hecke-Maass form, and {\gamma} a geodesic segment on X. We obtain a power saving over the local bound of Burq-G\'erard-Tzvetkov for the L^2 norm of ...
Critical partitions and nodal deficiency of billiard eigenfunctions
Critical partitions nodal deficiency billiard eigenfunctions Mathematical Physics
2011/9/14
Abstract: The paper addresses the the number of nodal domains for eigenfunctions of Schr\"{o}dinger operators with Dirichlet boundary conditions in bounded domains. In dimension one, the $n$th eigenfu...
Estimates on Neumann eigenfunctions at the boundary, and the "Method of Particular Solutions" for computing them
Estimates Neumann eigenfunctions Spectral Theory Analysis of PDEs
2011/9/1
Abstract: We consider the "Method of particular solutions" for numerically computing eigenvalues and eigenfunctions of the Laplacian $\Delta$ on a smooth, bounded domain Omega in RR^n with either Diri...
On the Geometry of the Nodal Lines of Eigenfunctions of the Two-Dimensional Torus
Geometry of the Nodal Lines of Eigenfunctions Two-Dimensional Torus
2011/2/22
The width of a convex curve in the plane is the minimal distance between a pair of parallel supporting lines of the curve. In this paper we study the width of nodal lines of eigenfunctions of the Lapl...
Eigenfunctions and Very Singular Similarity Solutions of Odd-Order Nonlinear Dispersion PDEs
Eigenfunctions Very Singular Similarity Solutions Odd-Order Nonlinear Dispersion PDEs
2010/11/11
Asymptotic properties of solutions of odd-order nonlinear dispersion equations are studied. The global in time similarity solutions, which lead to eigenfunctions of the rescaled ODEs, are constructed....
Concerning the $L^4$ norms of typical eigenfunctions on compact surfaces
typical eigenfunctions compact surfaces
2010/11/8
Let $(M,g)$ be a two-dimensional compact boundaryless Riemannian manifold with Laplacian, $\Delta_g$. If $e_\lambda$ are the associated eigenfunctions of $\sqrt{-\Delta_g}$ so that $-\Delta_g e_\lamb...
Eigenvalues and eigenfunctions of the Laplacian via inverse iteration with shift
Eigenvalues and eigenfunctions the Laplacian
2010/11/19
In this paper we present an iterative method inspired by the inverse iteration with shift technique of finite linear algebra designed to find the eigenvalues and eigenfunctions of the Laplacian with h...
Let M be a smooth closed Riemannian manifold and the Laplace operator. A function u is said to be an eigenfunction with eigenvalue if u = − u .
The semiclassical limit of eigenfunctions of the Schrödinger equation and the Bohr-Sommerfeld quantization condition, revisited
he semiclassical limit of eigenfunctions Schrö dinger equation Bohr-Sommerfeld quantization condition
2010/12/1
Consider the semiclassical limit, as the Planck constant ~ ! 0, of bound states of a quantum particle in a one-dimensional potential well. We justify the semiclassical asymptotics of eigenfunctions an...
On the Excursion Sets of Spherical Gaussian Eigenfunctions
Gaussian Eigenfunctions Excursion Sets Empirical Measure High Energy Asymptotics
2010/12/10
The high frequency behaviour for random eigenfunctions of the spherical Laplacian has been recently the object of considerable interest, also because of strong motivations arising from Physics and Cos...
On polygonal domains with trigonometric eigenfunctions of the Laplacian under Dirichlet or Neumann boundary conditions
polygonal domains trigonometric eigenfunctions
2010/9/14
A classification of all polygonal domains possessing a complete set of trigonometric eigenfunctions of the Laplacian under either Dirichlet or Neumann boundary conditions is developed. Polygonal domai...