Functional model for generalised resolvents and its application to time-dispersive media

Kirill Cherednichenko; Yulia Ershova; Sergey Naboko

doi:10.1007/s13324-024-00993-0

Functional model for generalised resolvents and its application to time-dispersive media

Kirill Cherednichenko, Yulia Ershova, Sergey Naboko

Research output: Contribution to journal › Article › peer-review

1 Citation (SciVal)

Abstract

Motivated by recent results concerning the asymptotic behaviour of differential operators with highly contrasting coefficients, whose effective descriptions have involved 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.

Original language	English
Article number	136
Number of pages	26
Journal	Analysis and Mathematical Physics
Volume	14
Issue number	6
Early online date	28 Nov 2024
DOIs	https://doi.org/10.1007/s13324-024-00993-0
Publication status	Published - 31 Dec 2024

Data Availability Statement

No datasets were generated or analysed during the current study.

Acknowledgements

We are grateful to Dr A. V. Kiselev for reading the paper and providing a number of insightful comments

Funding

KDC is grateful for the financial support of EPSRC Grants EP/L018802/2, EP/V013025/1. YYE and SNN acknowledge financial support by the Russian Science Foundation Grant No. 20-11-20032. KDC and YYE have been partially supported by CONACyT CF-2019 No. 304005. We are grateful to Dr A. V. Kiselev for reading the paper and providing a number of insightful comments.

Funders	Funder number
Russian Science Foundation	20-11-20032
Russian Science Foundation
Engineering and Physical Sciences Research Council	EP/L018802/2, EP/V013025/1
Engineering and Physical Sciences Research Council
Consejo Nacional de Humanidades, Ciencias y Tecnologías	CF-2019, 304005
Consejo Nacional de Humanidades, Ciencias y Tecnologías

Access to Document

10.1007/s13324-024-00993-0Licence: CC BY

https://arxiv.org/abs/2111.05387

Cite this

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abstract = "Motivated by recent results concerning the asymptotic behaviour of differential operators with highly contrasting coefficients, whose effective descriptions have involved 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.",

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AB - Motivated by recent results concerning the asymptotic behaviour of differential operators with highly contrasting coefficients, whose effective descriptions have involved 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.

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Functional model for generalised resolvents and its application to time-dispersive media

Abstract

Data Availability Statement

Acknowledgements

Funding

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Quantitative tools for upscaling the micro-geometry of resonant media

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory

Cite this

Functional model for generalised resolvents and its application to time-dispersive media

Abstract

Data Availability Statement

Acknowledgements

Funding

Access to Document

Other files and links

Fingerprint

Projects

Quantitative tools for upscaling the micro-geometry of resonant media

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory

Cite this