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1.
We analyze a general class of self-adjoint difference operators , where V
ε is a one-well potential and ε is a small parameter. We construct a Finslerian distance d induced by H
ε and show that short integral curves are geodesics. Then we show that Dirichlet eigenfunctions decay exponentially with a
rate controlled by the Finsler distance to the well. This is analog to semiclassical Agmon estimates for Schr?dinger operators.
Submitted: February 23, 2008. Accepted: May 23, 2008. 相似文献
2.
Mohammud Foondun 《Potential Analysis》2009,31(1):21-44
We consider the operator defined on functions by
Under the assumption that the local part of the operator is uniformly elliptic and with suitable conditions on n(x,h), we establish a Harnack inequality for functions that are nonnegative in and harmonic in a domain. We also show that the Harnack inequality can fail without suitable conditions on n(x,h). A regularity theorem for those nonnegative harmonic functions is also proved.
相似文献
3.
Weyl–Hörmander calculus is used to geta parametrix in OPS1/2,1/2
1–m
()for a class of subelliptic pseudodifferential operators in OPS1,0
m
()with real nonnegative principal symbol. 相似文献
4.
Chen Hua 《偏微分方程(英文版)》1990,3(2)
This paper studies the micro-local version of the Gevrey-hypoellipticity for a class of parabolic type operator, ∂_t-a(t, x; D_s,) (a(t, x;D_s) (a(t, x; ξ) ∈ C^∞([0, T], S^m_{G^m}(R^n)) (m ≥ 1/s) is a Gevrey-pseudoanaiytic symbol of class s(s > 1)), and we obtain the following main result: Under the condition (I), the operator stated above is micro-local Gevrey-hypoelliptic. In order to prove our main result, the auther have used (α, β) method in this paper. 相似文献
5.
6.
Rolando Gárciga Otero Alfredo Iusem 《Journal of Optimization Theory and Applications》2013,159(3):656-672
We introduce in this paper a new class of nonlinear operators, which contains, among others, the class of operators with semimonotone additive inverse and also the class of nonexpansive mappings. We study this class and discuss some of its properties. Then we present iterative procedures for computing fixed points of operators in this class, which allow for inexact solutions of the subproblems and relative error criteria. We prove weak convergence of the generated sequences in the context of Hilbert spaces. Strong convergence is also discussed. 相似文献
7.
Reducing Subspaces for a Class of Multiplication Operators 总被引:4,自引:0,他引:4
Let D be the open unit disk in the complex plane C. The Bergmanspace is the Hilbert space of analytic functions f in D such that
where dA is the normalized area measure on D. If
are two functions in , then the inner product of f and g is given by
We study multiplication operators on induced by analytic functions. Thus for H (D), the space ofbounded analytic functions in D, we define
by
It is easy to check that M is a bounded linear operator on with ||M||=||||=sup{|(z)|:zD}. 相似文献
8.
9.
We introduce and describe the characteristic class of a difference operator over the difference field (k((t)),). Here k is an algebraically closed field of characteristic zero and is the k-linear automorphism of k((t)) defined by (t)=t/(1+t). The approach is based on the characterization of simple difference operators in terms of their eigenvalues. 相似文献
10.
Ovidiu Furdui 《Integral Equations and Operator Theory》2008,60(4):469-483
In this paper we consider the space where dv
s
is the Gaussian probability measure. We give necessary and sufficient conditions for the boundedness of some classes of integral
operators on these spaces. These operators are generalizations of the classical Bergman projection operator induced by kernel
function of Fock spaces over .
相似文献
11.
This paper is the continuation of [1] in which complex symmetries of distributions and their covariance operators are investigated. Here we also study the most general quaternion symmetries of random vectors. Complete classification theorems on these symmetries are proved in terms of covariance operator spectra. 相似文献
12.
研究了奇型Sturm-Liouville算子的逆问题.对于固定的n∈N,证明了Sturm-Liouville问题(1.3)-(1.5)的第n个特征值λ_n(q,H)关于H是严格单调增加的,及一组不同边界条件下的第n个特征值的谱集合{λ_n(q,H_k)}_(k=1)~(+∞)能够唯一确定(0,πr)上的势函数q(x). 相似文献
13.
Siberian Mathematical Journal - We establish the criteria of validity of some integral weighted inequalities for a class of quasilinear integral operators. 相似文献
14.
Weighted Boundedness for a Class of Rough Multilinear Operators 总被引:8,自引:0,他引:8
In this paper we give the (L
p
(ω
p
), L
q
(ω
q
)) boundedness for a class of multilinear operators, which is simular to the higher-order commutator for the rough fractional
integral. In our results the kernel function is merely assumed on a size condition.
Received August 21, 2000, Accepted October 24, 2000 相似文献
15.
一类积—微分算子的离散本征值 总被引:2,自引:0,他引:2
本文讨论的积-微分算子是一类以众多应用领域为背景的无界、非自伴线性算子.在较一般的假设下,籍助L~2空间的线性算子理论,我们证明了这类算子存在离散本征值的充分条件,并获得了可供实际工作者参考的估计式. 相似文献
16.
Ukrainian Mathematical Journal - We establish Caccioppoli-type estimates for a class of nonlinear differential equations with the help of a differential identity that generalizes the well-known... 相似文献
17.
18.
In this paper, we study the equation \(\mathcal {L} u=0\) in \(\mathbb {R}^{N}\), where \(\mathcal {L}\) belongs to a general class of nonlocal linear operators which may be anisotropic and nonsymmetric. We classify distributional solutions of this equation, thereby extending and generalizing recent Liouville type theorems in the case where \(\mathcal {L}= (-{\Delta })^{s}\), s ∈ (0, 1) is the classical fractional Laplacian. 相似文献
19.
We establish the basis of a discrete function theory starting with a Fischer decomposition for difference Dirac operators.
Discrete versions of homogeneous polynomials, Euler and Gamma operators are obtained. As a consequence we obtain a Fischer
decomposition for the discrete Laplacian. 相似文献
20.
We develop a theoretical framework for projection-iterative methods to solve operator equations of the form Au + Bu = f, where A is a Toeplitz operator in a Banach space , B is considered as a perturbation (of general form) of A, and f is a given element in this space. The methods are adopted for application to general situations, in particular, to the equations
in which A need not be a Fredholm operator. The idea to involve iteration procedures and the technique which we apply allow to obtain
conditions on perturbations for convergence and effective error estimates in terms of some weighted spaces (without any restrictions
on the norms for perturbations). Based on established evaluations we derive further information about decaying properties
of the solutions. The obtained results are illustrated by considering concrete classes of equations as, for instance, equations
corresponding to Jacobi type operators.
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