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...
We give a sufficient condition for a self-adjoint operator to have the following properties in a neighborhood of a pointE of its spectrum:a) its point spectrum is finite; b) its singular continuous spectrum is empty; c) its resolvent sat... ...
the operator −Δ + q(x) in the space L 2 (E 2 k) (k ≥1) where q(x) is a measurable complex-valued function satisfying the condition ¦q(x) ¦ ≤Ce −ɛ¦x¦ , having no finite limit points, and for k=1 the discrete spectrum consists of a finite number of ...
Operator Theory:Advances and Applications, Vol. 175, 121–158c ? 2007 Birkh¨ auser Verlag Basel/SwitzerlandOn the Spectrum of the Self-adjointExtensions of a Nonnegative Linear Relationof Defect One in a Krein SpaceP. Jonas and H. LangerAbstract. A nonnegative symmetric linear relation A 0...
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On the Essential Spectrum of a Class of Singular Self-adjoint Differential Operators 一类奇异自伴微分算子的本质谱 service.ilib.cn 3. Isolate Point of Operator Essential Spectrum in the Approximation for Bounded Linear Operator 有界线性算子逼近问题中算子本质谱孤立点的处理 www.ilib.cn 4. Components ...
We characterize the set of diagonals of the unitary orbit of a self-adjoint operator with three points in the spectrum. Our result gives a Schur-Horn theor... Jasper,John - 《Journal of Functional Analysis》 被引量: 39发表: 2013年 The Schur-Horn Theorem for operators with finite spectrum ...
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》 ...
trum of this multiplication operator is continuous and given by the closure of the range of the multiplying func- tion. This proves that P 0 is a bounded self-adjoint op- erator on the Hilbert space CLL 2 (R + , µ) with spectrum σ(P 0 ) = σ c (P 0 ) = [0, 1]. To ...
of self-adjoint Sturm–Liouville and Dirac operators and presented a discrete analogue of system (1.1) using the method of finite differences. If the functions\(p_{ik} ( x ) \)(\(i,k= 1,2 \)) are complex valued, then the operatorTis called nonselfadjoint. Also, if the operatorTis...