Asymptotic analysis of operator families and applications to resonant media

Kirill D. Cherednichenko, Yulia Yu Ershova, Alexander V. Kiselev, Vladimir A. Ryzhov, Luis O. Silva

Research output: Chapter or section in a book/report/conference proceedingChapter or section

3 Citations (SciVal)
75 Downloads (Pure)

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 languageEnglish
Title of host publicationFrom Complex Analysis to Operator Theory
Subtitle of host publicationA Panorama
EditorsM. Brown, F. Gesztesy, P. Kurasov, A. Laptev, B. Simon, G. Stolz, I. Wood
Place of PublicationCham, Switzerland
PublisherBirkhäuser
Pages239-311
Number of pages73
ISBN (Electronic)9783031311390
ISBN (Print)9783031311383
DOIs
Publication statusPublished - 21 Apr 2023

Publication series

NameOperator Theory: Advances and Applications
Volume291
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:1510.03364

Funding

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

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