TY - JOUR

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

AU - Cherednichenko, K.D.

AU - Ershova, Y.Y.

AU - Naboko, S.N.

N1 - Export Date: 01 November 2025; Cited By: 1; Correspondence Address: K.D. Cherednichenko; Department of Mathematical Sciences, University of Bath, Bath, Claverton Down, BA2 7AY, United Kingdom; email: k.cherednichenko@bath.ac.uk

PY - 2024

Y1 - 2024

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. © 2024 Elsevier B.V., All rights reserved.

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. © 2024 Elsevier B.V., All rights reserved.

U2 - 10.1007/s13324-024-00993-0

DO - 10.1007/s13324-024-00993-0

M3 - статья

VL - 14

JO - Analysis and Mathematical Physics

JF - Analysis and Mathematical Physics

SN - 1664-2368

IS - 6

ER -