This chapter contains multiple tools for studying the spectrum of a self-adjoint operator. First, we discuss how the spectrum is modified when a small perturbation is added to a given operator. Next, we define the different types of spectrum (point, continuous, essential, discrete) and present...
linear operator 线性算子,线性运算器 linear partial differential operator 线性偏微分算子 linear differential operator 线性微分算符 symmetric linear operator 对称线性算子 complete linear operator 完全线性算子 conjugate linear operator 共轭线性算符 closed linear operator 闭线性算子 adjoint linear operator...
The spectrum and essential spectrum of a self-adjoint operator in a real Hilbert space are characterized in terms of Palais–Smale conditions on its quadratic form and Rayleigh quotient respectively.doi:10.1112/S0024610799008455StuartC. A.Oxford University Press (OUP)Journal of the London Mathematical...
Technique is given for determining the asymptotic properties of vectors which are perturbations of a given basis-theeigenfunctions a selfadjoint operator. Its application is illustratedby a differential equation example, not using the Hu... EG Effros,JL Kazdan - 《Indiana University Mathematics Journal...
We study the spectrum of low-lying eigenmodes of the kinetic operator for scalar particles, in the color adjoint representation of Yang-Mills theory. The kinetic operator is the covariant Laplacian, plus a constant which serves to renormalize mass. In the pure gauge theory, our data indicates ...
Circular dichotomy of the spectrum of a certain class of non-selfadjoint operators Let H be a complex Hilbert space, and let U and B be two operators on the Banach algebra EndH of linear bounded operators acting on H. We assume that everywhere below the operator U as being unitary, the...
线性算子的谱分解吮暇喇decomp佣i“佣of a linear叩erator;cneKTPa几I.ltoe Pa3几0搜e”一e月I.He幼ItoroonePaTOPa] 一个线性算子的关于谱测度(spectral此asure)(谱分解(spect司~加石。n))的一个积分形式的表示.对Hilbert空间H上任何自伴算子(留甘一adjointOPerator)T有一个谱分解尸(·),使得 :一f。
An investigation is made of the operator pencil under the assumption that the selfadjoint operators , , and satisfy the strong damping condition . Such operator pencils have been studied thoroughly in the literature under the condition t... Shkalikov,A A - 《Mathematics of the Ussr Sbornik》 ...
With every $J$-frame theso-called $J$-frame operator is associated, which is a self-adjoint operator inthe Krein space $\mathcal{H}$. The $J$-frame operator plays an essential rolein the indefinite reconstruction formula. In this paper we characterize the class of $J$-frame operators ...
{+},其中 \mathbf{R}_x 是相关算子(即,核为 R_x\left(t_1, t_2\right) 的正定或半定(positive definite or semidefinite, self-adjoint linear operator )的自伴线性算子), \boldsymbol{\Phi} 是核为 \phi(t, f) 的线性算子,\boldsymbol{\Phi}^{+} 是算子 \Phi 的adjoint of the operator[...