Discrete scaling based on operator theory

It is well known that for an associative ring R, if ab has g-Drazin inverse then ba has g-Drazin inverse. In this case, (ba)d = b((ab)d)2a. This formula is so-called Cline?s formula for g-Drazin inverse, which plays an elementary role in matrix and operator theory. In this paper, we generalize Cline?s formula to the wider case. In particular, as applications, we obtain new common spectral properties of bounded linear operators.

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Quantum Resonances: Line Profiles and Dynamics

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc20030529 ◽

2003 ◽

Vol 68 (3) ◽

pp. 529-553 ◽

Cited By ~ 3

Author(s):

Ivana Paidarová ◽

Philippe Durand

Keyword(s):

Hydrogen Atom ◽

Operator Theory ◽

Quantum Dynamics ◽

Line Profiles ◽

Static Electric Field ◽

Reversal Effect ◽

Quantum Resonances ◽

Energy Dependent ◽

Effective Hamiltonians

The wave operator theory of quantum dynamics is reviewed and applied to the study of line profiles and to the determination of the dynamics of interacting resonances. Energy-dependent and energy-independent effective Hamiltonians are investigated. The q-reversal effect in spectroscopy is interpreted in terms of interfering Fano profiles. The dynamics of an hydrogen atom subjected to a strong static electric field is revisited.

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Operator theory on quaternionic Hilbert spaces

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700045032 ◽

1972 ◽

Vol 7 (2) ◽

pp. 297-299

Author(s):

Neil Charles Powers

Keyword(s):

Hilbert Spaces ◽

Operator Theory

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Regular approximation of singular Sturm–Liouville problems with eigenparameter dependent boundary conditions

Boundary Value Problems ◽

10.1186/s13661-019-01316-0 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Maozhu Zhang ◽

Kun Li ◽

Hongxiang Song

Keyword(s):

Boundary Conditions ◽

Operator Theory ◽

Resolvent Convergence ◽

Spectral Inclusion ◽

Regular Approximation ◽

Special Cases ◽

Abstract Operator ◽

Norm Resolvent Convergence ◽

Sturm Liouville ◽

Spectral Exactness

AbstractIn this paper we consider singular Sturm–Liouville problems with eigenparameter dependent boundary conditions and two singular endpoints. The spectrum of such problems can be approximated by those of the inherited restriction operators constructed. Via the abstract operator theory, the strongly resolvent convergence and norm resolvent convergence of a sequence of operators are obtained and it follows that the spectral inclusion of spectrum holds. Moreover, spectral exactness of spectrum holds for two special cases.

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Analyzing Effectiveness of Gang Interventions using Koopman Operator Theory

2020 IEEE International Conference on Big Data (Big Data) ◽

10.1109/bigdata50022.2020.9378297 ◽

2020 ◽

Author(s):

Sian Wen ◽

Andy Chen ◽

Tanishq Bhatia ◽

Nicholas Liskij ◽

David Hyde ◽

...

Keyword(s):

Operator Theory ◽

Koopman Operator ◽

Gang Interventions

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Existence results for a class of random delay integrodifferential equations

Random Operators and Stochastic Equations ◽

10.1515/rose-2021-2054 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Amadou Diop ◽

Mamadou Abdul Diop ◽

K. Ezzinbi

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Operator Theory ◽

Mild Solutions ◽

Random Delay ◽

Random Fixed Point ◽

Unbounded Delay ◽

Carathéodory Conditions ◽

Random Fixed Point Theorem

Abstract In this paper, we consider a class of random partial integro-differential equations with unbounded delay. Existence of mild solutions are investigated by using a random fixed point theorem with a stochastic domain combined with Schauder’s fixed point theorem and Grimmer’s resolvent operator theory. The results are obtained under Carathéodory conditions. Finally, an example is provided to illustrate our results.

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