平板几何迁移算子的特征值问题

研究L^p(1相似文献   

A note on the eigenvalues of p‐fractional Hardy–Sobolev operator with indefinite weight

In this article, we study the eigenvalues of p‐fractional Hardy operator where , , , and Ω is an unbounded domain in with Lipschitz boundary containing 0. The weight function V may change sign and may have singular points. We also show that the least positive eigenvalue is simple and it is uniquely associated to a nonnegative eigenfunction. Moreover, we proved that there exists a sequence of eigenvalues as .     

Lower bound for the ratios of eigenvalues of Schrödinger with nonpositive single‐barrier potentials

Horváth and Kiss (Proc. Amer. Math. Soc., 2005) proved the upper bound estimate for Dirichlet eigenvalue ratios of the Schrödinger problem ?y^′′ + q(x)y = λy with nonnegative and single‐well potential q. In this paper, we prove that if q(x) is a nonpositive, continuous, and single‐barrier potential, then for λ_n > λ_m≥ ? 2q^?, where . In particular, if q(x) satisfies the additional condition , then λ₁ > 0 and for n > m ≥ 1. For this result, we develop a new approach to study the monotonicity of the modified Prüfer angle function.     

An alternative proof of lower bounds for the first eigenvalue on manifolds

Recently, Andrews and Clutterbuck [1] gave a new proof of the optimal lower eigenvalue bound on manifolds via modulus of continuity for solutions of the heat equation. In this short note, we give an alternative proof of Theorem 2 in [1]. More precisely, following Ni's method (Section 6 of [5]), we give an elliptic proof of this theorem.     

Approximations of spectra of Schrödinger operators with complex potentials on ℝd

We study spectral approximations of Schrödinger operators T = ?Δ+Q with complex potentials on Ω = ?^d, or exterior domains Ω??^d, by domain truncation. Our weak assumptions cover wide classes of potentials Q for which T has discrete spectrum, of approximating domains Ω_n, and of boundary conditions on ?Ω_n such as mixed Dirichlet/Robin type. In particular, Re Q need not be bounded from below and Q may be singular. We prove generalized norm resolvent convergence and spectral exactness, i.e. approximation of all eigenvalues of T by those of the truncated operators T_n without spectral pollution. Moreover, we estimate the eigenvalue convergence rate and prove convergence of pseudospectra. Numerical computations for several examples, such as complex harmonic and cubic oscillators for d = 1,2,3, illustrate our results.     

椭圆PDE-约束优化问题的一个预条件子

针对由Galerkin有限元离散椭圆PDE-约束优化问题产生的具有特殊结构的3×3块线性鞍点系统,提出了一个预条件子并给出了预处理矩阵特征值及特征向量的具体表达形式.数值结果表明了该预条件子能够有效地加速Krylov子空间方法的收敛速率,同时也验证了理论结果.     

On the first eigenvalue of the mean finsler-laplacian

In this paper, we prove that several different definitions of the Finsler-Laplacian are equivalent. Then we prove that any Berwald metric is affinely equivalent to its mean metric and give some upper or lower bound estimates for the first eigenvalue of the mean Laplacian on Berwald manifolds, which generalize some results in Riemannian geometry.     

关于稳定矩阵分解定理的一个简单证明

一个矩阵称为稳定的,如果这个矩阵的特征值全包含在单位开圆盘内.利用Parker关于复方阵的分解定理给出了稳定矩阵分解定理的一个简单证明,并对奇异值全部严格小于1的矩阵给出了类似的结论.