Generalized Radon--Nikodym Spectral Approach. Application to Relaxation Dynamics Study.

@article{Bobyl2016GeneralizedRS,
  title={Generalized Radon--Nikodym Spectral Approach. Application to Relaxation Dynamics Study.},
  author={Aleksandr Bobyl and Andrei Georgievich Zabrodskii and Mikhail Evgenievich Kompan and Vladislav Gennadievich Malyshkin and O. Novikova and E. E. Terukova and Dmitry V. Agafonov},
  journal={Econometrics: Mathematical Methods \& Programming eJournal},
  year={2016}
}
Radon--Nikodym approach to relaxation dynamics, where probability density is built first and then used to calculate observable dynamic characteristic is developed and applied to relaxation type signals study. In contrast with L² norm approaches, such as Fourier or least squares, this new approach does not use a norm, the problem is reduced to finding the spectrum of an operator (virtual Hamiltonian), which is built in a way that eigenvalues represent the dynamic characteristic of interest and… 
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6 Citations
Background Citations
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28 References

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