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

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
Early online date	28 Nov 2024
DOIs	https://doi.org/10.1007/s13324-024-00993-0
Publication status	Published - 28 Nov 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

Access to Document

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

https://arxiv.org/abs/2111.05387

Quantitative tools for upscaling the micro-geometry of resonant media
Cherednichenko, K. (PI)
Engineering and Physical Sciences Research Council
1/11/21 → 31/10/24
Project: Research council

Cite this

@article{14c0b61a4d5c45a482c0b0994ca50b06,

title = "Functional model for generalised resolvents and its application to time-dispersive media",

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.",

author = "Kirill Cherednichenko and Yulia Ershova and Sergey Naboko",

year = "2024",

month = nov,

day = "28",

doi = "10.1007/s13324-024-00993-0",

language = "English",

volume = "14",

journal = "Analysis and Mathematical Physics",

issn = "1664-2368",

publisher = "Birkhauser",

}

TY - JOUR

T1 - Functional model for generalised resolvents and its application to time-dispersive media

AU - Cherednichenko, Kirill

AU - Ershova, Yulia

AU - Naboko, Sergey

PY - 2024/11/28

Y1 - 2024/11/28

N2 - 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.

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.

U2 - 10.1007/s13324-024-00993-0

DO - 10.1007/s13324-024-00993-0

M3 - Article

SN - 1664-2368

VL - 14

JO - Analysis and Mathematical Physics

JF - Analysis and Mathematical Physics

M1 - 136

ER -

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

Abstract

Data Availability Statement

Acknowledgements

Access to Document

Fingerprint

Projects

Quantitative tools for upscaling the micro-geometry of resonant media

Cite this