Results 171 to 180 of about 1,194 (210)
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Computing the Spectrum and Representing the Resolvent
Numerical Functional Analysis and Optimization, 2009We discuss computing the spectrum of a bounded operator and representing its resolvent operator. The results include a general convergence theorem for the polynomial convex hull of the spectrum and explicit representations for the resolvent outside. The results are formulated and proved in general Banach algebras.
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1978
The eigenvalues of an n × n matrix M constitute a (finite) point set in the complex plane, called the spectrum of M. If A is any linear operator in a Hilbert space ℌ, the complex plane ℂ is similarly decomposed into two parts: the spectrum of A, denoted by σ(A), and the resolvent set, denoted by ρ(A).
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The eigenvalues of an n × n matrix M constitute a (finite) point set in the complex plane, called the spectrum of M. If A is any linear operator in a Hilbert space ℌ, the complex plane ℂ is similarly decomposed into two parts: the spectrum of A, denoted by σ(A), and the resolvent set, denoted by ρ(A).
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The Resolvent and The Spectrum
2009A large, and the most important, part of operator theory is the study of the spectrum of an operator. In finite dimensions, this is the set of eigenvalues of A. In infinite dimensions there are complications that arise from the fact that an operator could fail to be invertible in different ways.
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Vibrationally Resolved LIF Spectrum of Tertiary Methylcyclohexoxy Radical
The Journal of Physical Chemistry A, 2012Cyclohexoxy radical and its substitutes are intermediates of the combustion reaction in automobile engines, and hence play an important role in the atmospheric chemistry. Spectroscopic and conformational studies can provide convenient methods to monitor these species.
Qijun, Wu +3 more
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1965
Let T be a linear operator whose domain D(T) and range R(T) both lie in the same complex linear topological space X. We consider the linear operator $${T_\lambda } = \lambda I - T,$$ , where λ is a complex number and I the identity operator. The distribution of the values of λ for which T λ has an inverse and the properties of the inverse when ...
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Let T be a linear operator whose domain D(T) and range R(T) both lie in the same complex linear topological space X. We consider the linear operator $${T_\lambda } = \lambda I - T,$$ , where λ is a complex number and I the identity operator. The distribution of the values of λ for which T λ has an inverse and the properties of the inverse when ...
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Spectrum Resolved SNR Monitoring of In-Service Channel
Optical Fiber Communication Conference (OFC) 2024We propose and experimentally demonstrate a novel scheme to monitor the spectrum resolved SNR with receiver ADC buffer data. SNR accuracy of 0.2dB can be achieved, and filtering impact can be separated from link noise.
Qingyi Guo +3 more
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Time-resolved electron spectrum measurements on the FELIX facility
Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 1993Measurements of the FELIX electron energy spectrum using multichannel secondary emission monitors are described. The detectors have a time resolution of 50 ns and span typically 4% in electron energy over 32 channels. Aspects of the design of the OTR detector and energy spectrometer for FELIX are presented, along with data recently acquired with the ...
Gillespie, W.A. +7 more
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Resolving the Optical Spectrum of Water: Coordination and Electrostatic Effects
Physical Review Letters, 2008The optical absorption of small water clusters, water chains, liquid water, and crystalline ice is analyzed computationally. We identify two competing mechanisms determining the onset of the optical absorption: Electronic transitions involving surface molecules of finite clusters or chains cause a redshift upon molecular aggregation compared to ...
A, Hermann +2 more
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Spectrum, Resolvent and Analytic Functional Calculus
1989From the point of wiev of the general spectral theory of linear operators, the hyponormality condition has several important and rather unexpected consequences. Among these we mention the formula for the spectral radius, the estimates of the resolvent function, as well as other results such as the existence of the scalar extension and Dynkin’s analytic
Mircea Martin, Mihai Putinar
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Spectrum, Resolvent and Power Boundedness
1993Let L be a bounded operator in a complex Banach space X. In this space we denote the norm by ‖⋅‖ and the same notation is used for the induced operator norms. Unless explicitly stated otherwise, continuity, convergence etc. is to be understood in terms of the norm topology in X and in the uniform operator topology for operators.
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