Projects per year
Abstract
We give an overview of operator-theoretic tools that have recently proved useful in the analysis of boundary-value and transmission problems for second-order partial differential equations, with a view to addressing, in particular, the asymptotic behaviour of resolvents of physically motivated parameter-dependent operator families. We demonstrate the links of this rich area, on the one hand, to functional frameworks developed by S. N. Naboko and his students, and on the other hand, to concrete applications of current interest in the physics and engineering communities.
Original language | English |
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Title of host publication | From Complex Analysis to Operator Theory |
Subtitle of host publication | A Panorama |
Editors | M. Brown, F. Gesztesy, P. Kurasov, A. Laptev, B. Simon, G. Stolz, I. Wood |
Place of Publication | Cham, Switzerland |
Publisher | Birkhäuser |
Pages | 239-311 |
Number of pages | 73 |
ISBN (Electronic) | 9783031311390 |
ISBN (Print) | 9783031311383 |
DOIs | |
Publication status | Published - 21 Apr 2023 |
Publication series
Name | Operator Theory: Advances and Applications |
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Volume | 291 |
ISSN (Print) | 0255-0156 |
ISSN (Electronic) | 2296-4878 |
Bibliographical note
62 pages, 2 figures; a survey of recent results in the area, see also arXiv:2010.13318, arXiv:1808.03961, arXiv:1703.06220, arXiv:1510.03364Funding
Acknowledgments KDC, AVK have been supported by EPSRC (Grants EP/L018802/2, EP/V013025/1.) The work of all authors has been supported by CONACyT CF-2019 No. 304005.
Keywords
- Dissipative operators
- Functional models
- Generalised resolvents
- Homogenisation
- Inverse scattering problem
- Quantum graphs
- Resonant media
- Wave propagation
- Zero-range models
ASJC Scopus subject areas
- Analysis
Fingerprint
Dive into the research topics of 'Asymptotic analysis of operator families and applications to resonant media'. Together they form a unique fingerprint.Projects
- 3 Finished
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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
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Newton Mobility Grant -: Homogenisation of Degenerate Equations and Scattering for New Materials
Cherednichenko, K. (PI)
1/02/17 → 31/01/19
Project: Research council
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Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory
Cherednichenko, K. (PI)
Engineering and Physical Sciences Research Council
23/07/14 → 22/06/19
Project: Research council