Results 161 to 170 of about 18,799 (180)

Resolvent and Spectrum

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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The Resolvent and The Spectrum

2009
A 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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Spectrum, Resolvent and Power Boundedness

1993
Let 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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Time-resolved electron spectrum measurements on the FELIX facility

Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 1993
Measurements 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., Martin, P.F., MacLeod, A.M., Macdonald, A.J., Bakker, R.J., van der Geer, C.A. J., van der Meer, A.F. G., van Amersfoort, P.W.   +7 more
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Direct Picosecond Resolving of Hot Luminescence Spectrum

1982
Hot luminescence |1| (HL) as a natural by-product of relaxation within excited electronic states enables relaxation kinetics to be investigated in detail without recourse to applying any additional (probing) action on the system, which may disturb the process under study. For systems possessing distinct-structured vibronic spectra (e.g.
J. Aaviksoo, A. Anijalg, A. Freiberg, M. Lepik, P. Saari, T. Tamm, K. Timpmann   +6 more
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The spectrum of ?-resolvable designs with block size four

Journal of Combinatorial Designs, 2001
A design is called \(\alpha\)-resolvable if its blocks can be partitioned into disjoint classes such that each point is on exactly \(\alpha\) blocks of any given class. The authors prove that the necessary arithmetic conditions for the existence of an \(\alpha\)-resolvable design with block size 4 are also sufficient, with the single exception of ...
Vasiga, Troy M. J., Furino, Steven, Ling, Alan C. H.   +2 more
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The rotationally resolved electronic spectrum of p-cyanophenol

Phys. Chem. Chem. Phys., 2002
The electronic origin transition of p-cyanophenol (4-hydroxy-benzonitrile) at 35547.46 cm−1 was examined using rotationally resolved LIF spectroscopy. The experimentally determined inertial parameters are reported and compared to the results of ab initio calculations. The S1-lifetime of p-cyanophenol is determined to be 10.6 ± 3 ns, considerably longer
Jochen Küpper, Michael Schmitt, Karl Kleinermanns   +2 more
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Vibrationally resolved Si 2p photoabsorption spectrum of SiF4

Chemical Physics Letters, 1996
Abstract A high-resolution study of the Si 2p photoabsorption spectrum of gas-phase SiF 4 is reported. In the excitation region of the Rydberg orbitals, vibrational substates from symmetric stretching vibrational modes were resolved, which were described on the basis of a Franck-Condon analysis resulting in vibrational energies and equilibrium ...
R. Püttner, M. Domke, K. Schulz, G. Kaindl   +3 more
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Vibrationally resolved O 1s photoelectron spectrum of water

Chemical Physics Letters, 2003
Abstract The O 1s photoelectron spectrum of water was recorded with the resolution high enough to resolve the vibrational structure of the O 1s −1 state and the lifetime width and the Franck-Condon (FC) factors were extracted. The experimental spectrum was reproduced well by the molecular ab initio calculations based on the symmetry adapted cluster ...
Sankari, R, Ehara, M, Nakatsuji, H, Senba, Y, Hosokawa, K, Yoshida, H, De Fanis, A, Tamenori, Y, Aksela, S, Ueda, K   +9 more
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Computing the Spectrum and Representing the Resolvent

Numerical Functional Analysis and Optimization, 2009
We 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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