Results 221 to 230 of about 499 (268)
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2020
This chapter introduces the notion of the spectrum of an operator (possibly unbounded) on a Hilbert space. The theory of the resolvent operator is developed and used to establish basic properties of the spectrum.
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This chapter introduces the notion of the spectrum of an operator (possibly unbounded) on a Hilbert space. The theory of the resolvent operator is developed and used to establish basic properties of the spectrum.
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Resolved pseudo-raman spectrum of ovuline albumin
Chemical Physics Letters, 1974Abstract A series of resolved pseudo-Raman peaks, in harmonic position, is obtained from ovuline albumin. The spectrum is a function of the water layer bonded to the molecule. Data are in agreement with the theory of “electromagnetic molecular electronic resonance”.
J.P. Biscar, N. Kollias
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The first rotationally resolved spectrum of CH4+
The Journal of Chemical Physics, 1999The pulsed-field-ionization (PFI) zero-kinetic-energy (ZEKE) photoelectron spectra of CH4 and CD4 have been recorded in the region 100880–104100 cm−1. From the analysis of the photoelectron spectra the first adiabatic ionization potential of CH4 and CD4 has been determined to be (101773±35) cm−1 and (102210±25) cm−1, respectively.
R. Signorell, F. Merkt
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Time-resolved phosphorescence spectrum of propynal vapor
Journal of Molecular Spectroscopy, 1989Abstract The phosphorescence spectrum of gaseous propynal (HCCCHO) is measured by time-resolved techniques following pulsed ( T 1 via direct optical pumping into the S 0 → T 1 absorption transition and (ii) four single vibronic levels (SVL) of S 1 ( O 0 , 6 1 , 4 1 , and 2 1 ).
G.H. Atkinson +4 more
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Time-resolved fluorescence spectrum of Quinacrine Mustard
Optics Communications, 1980Abstract Time-resolved fluorescence spectrum of Quinacrine Mustard in acetate buffer solution (pH 4.6) under excitation of subnanosecond laser pulses is reported. The decay curve has been found to consist of three exponential components, whose amplitudes depend on both excitation and observation wavelengths.
A. Andreoni +3 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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RF spectrum congestion: Resolving an interference case
2011 IEEE International Conference on Microwaves, Communications, Antennas and Electronic Systems (COMCAS 2011), 2011Radio frequency spectrum monitoring and measurement is an important part of spectrum management that secures its safe and efficient use. In this paper we discuss the effects of insatiable hunger for RF spectrum resource especially in certain frequency bands. Such spectrum congestion causes a number of interference cases that has to be solved. We report
Dusan Jokanovic, Milos Josipovic
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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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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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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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