Functional model for generalised resolvents and its application to time-dispersive media
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| Format: | Preprint |
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2021
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| _version_ | 1866910683909586944 |
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| author | Cherednichenko, Kirill D. Ershova, Yulia Yu. Naboko, Sergey N. |
| author_facet | Cherednichenko, Kirill D. Ershova, Yulia Yu. Naboko, Sergey N. |
| contents | Motivated by recent results concerning the asymptotic behaviour of differential operators with highly contrasting coefficients, which have involved effective descriptions involving generalised resolvents, we construct the functional model for a typical example of the latter. This provides a spectral representation for the generalised resolvent, which can be utilised for further analysis, in particular the construction of the scattering operator in related wave propagation setups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_05387 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Functional model for generalised resolvents and its application to time-dispersive media Cherednichenko, Kirill D. Ershova, Yulia Yu. Naboko, Sergey N. Spectral Theory Mathematical Physics Functional Analysis Motivated by recent results concerning the asymptotic behaviour of differential operators with highly contrasting coefficients, which have involved effective descriptions involving generalised resolvents, we construct the functional model for a typical example of the latter. This provides a spectral representation for the generalised resolvent, which can be utilised for further analysis, in particular the construction of the scattering operator in related wave propagation setups. |
| title | Functional model for generalised resolvents and its application to time-dispersive media |
| topic | Spectral Theory Mathematical Physics Functional Analysis |
| url | https://arxiv.org/abs/2111.05387 |