The main concepts related to the spectrum of a linear operator are presented, including the resolvent set, and the division of the spectrum into point, continuous and residual spectrum. A number of examples are discussed in detail. General properties of the spectrum are studied, with special ...
Invertibility of multipliers and the spectrum of an operator in spaces with different norms 来自 Semantic Scholar 喜欢 0 阅读量: 20 作者: IY Shneiberg 摘要: Invertibility of multipliers and the spectrum of an operator in spaces with different norms ...
J. , The spectrum of an interpolated operator and analytic multivalued functions, Pacific J. Math. 121 (... TJ Ransford - 《Pacific Journal of Mathematics》 被引量: 13发表: 1986年 Estimation of multivalued arrivals in 3D models using wavefront construction—Part I A new 3D wavefield ...
Under these assumptions it is shown that thespectrum of the operator is absolutely continuous. Previously known results onabsolute continuity for periodic operators were obtained for the zero magneticflux.doi:10.4171/JST/102N. D. FilonovA. V. Sobolev...
This in turn shows that the restriction of the operator H to the half-line [0,+∞) (with any self-adjoint boundary condition at zero) has no essential spectrum on the interval I.Footnote 4 Similar arguments show that the half-line operator obtained by restriction of H to (−∞,0] (...
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The local resolvent set, ρT(x), of an operator T∈B(H) at a point x∈H is the union of all open subsets U of the complex plane C for which there is an analytic function ϕ:U→H such that (T−λ)ϕ(λ)=x (λ∈U). Clearly ρT(x) contains the resolvent set ρ(T)...
IfTis a linear operator of a normed spaceXto itself andIis the identity transformation (I(x) ≡x), the spectrum ofTconsists of all scalars λ for which eitherT- λIhas no inverse or the range ofT- λIis not dense inX. (physics) ...
On the Spectrum of the Discrete Schrödinger Operator of a Rank-Two Perturbation on Z. Lobachevskii J Math 45, 4874–4887 (2024). https://doi.org/10.1134/S1995080224606052 Download citation Received13 June 2024 Revised14 July 2024 Accepted21 August 2024 Published25 February 2025 Issue Date...
For an operator 𝑇 acting from an infinite-dimensional Hilbert space 𝐻 to a normed space 𝑌 we define the upper AMD-number and the lower AMD-number as the upper and the lower limit of the net ( δ (𝑇| 𝐸 )) 𝐸∈𝐹𝐷(𝐻) , with respect