Topological obstructions to the diagonalisation of pseudodifferential systems

Matteo Capoferri; Grigori Rozenblum; Nikolai Saveliev; Dmitri Vassiliev

doi:10.1090/bproc/147

Topological obstructions to the diagonalisation of pseudodifferential systems

Matteo Capoferri, Grigori Rozenblum, Nikolai Saveliev, Dmitri Vassiliev

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

3 Citations (Scopus)

31 Downloads (Pure)

Abstract

Given a matrix pseudodifferential operator on a smooth manifold,
one may be interested in diagonalising it by choosing eigenvectors of its principal symbol in a smooth manner. We show that diagonalisation is not always possible, on the whole cotangent bundle or even in a single fibre. We identify global and local topological obstructions to diagonalisation and examine physically meaningful examples demonstrating that all possible scenarios can occur.

Original language	English
Pages (from-to)	472-486
Number of pages	15
Journal	Proceedings of the American Mathematical Society: Series B
Volume	9
Issue number	43
DOIs	https://doi.org/10.1090/bproc/147
Publication status	Published - 27 Dec 2022

Keywords

math.AP
math-ph
math.MP
primary 58J40, secondary 35G35, 35J46, 35J47, 35J48

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Geometry and Topology
Algebra and Number Theory

Access to Document

10.1090/bproc/147Licence: CC BY

Download pdf
©2022 by the author(s) under Creative Commons Attribution 3.0 License (CC BY 3.0).
Final published version, 244 KBLicence: CC BY

Cite this

@article{a3739b981d2b41039e89c48f10aee0f3,

title = "Topological obstructions to the diagonalisation of pseudodifferential systems",

abstract = "Given a matrix pseudodifferential operator on a smooth manifold,one may be interested in diagonalising it by choosing eigenvectors of its principal symbol in a smooth manner. We show that diagonalisation is not always possible, on the whole cotangent bundle or even in a single fibre. We identify global and local topological obstructions to diagonalisation and examine physically meaningful examples demonstrating that all possible scenarios can occur.",

keywords = "math.AP, math-ph, math.MP, primary 58J40, secondary 35G35, 35J46, 35J47, 35J48",

author = "Matteo Capoferri and Grigori Rozenblum and Nikolai Saveliev and Dmitri Vassiliev",

note = "Funding Information: The first author was partially supported by the Leverhulme Trust Research Project Grant RPG-2019-240 and by a Heilbronn Small Grant (via the UKRI/EPSRC Additional Funding Programme for Mathematical Sciences). The second author was supported by a grant from Ministry of Science and Higher Education of RF, Agreement 075-15-2022-287. The third author was partially supported by NSF Grant DMS-1952762. The first author is the corresponding author. Publisher Copyright: {\textcopyright} 2022 by the author(s).",

year = "2022",

month = dec,

day = "27",

doi = "10.1090/bproc/147",

language = "English",

volume = "9",

pages = "472--486",

journal = "Proceedings of the American Mathematical Society: Series B",

issn = "2330-1511",

publisher = "American Mathematical Society",

number = "43",

}

TY - JOUR

T1 - Topological obstructions to the diagonalisation of pseudodifferential systems

AU - Capoferri, Matteo

AU - Rozenblum, Grigori

AU - Saveliev, Nikolai

AU - Vassiliev, Dmitri

N1 - Funding Information: The first author was partially supported by the Leverhulme Trust Research Project Grant RPG-2019-240 and by a Heilbronn Small Grant (via the UKRI/EPSRC Additional Funding Programme for Mathematical Sciences). The second author was supported by a grant from Ministry of Science and Higher Education of RF, Agreement 075-15-2022-287. The third author was partially supported by NSF Grant DMS-1952762. The first author is the corresponding author. Publisher Copyright: © 2022 by the author(s).

PY - 2022/12/27

Y1 - 2022/12/27

N2 - Given a matrix pseudodifferential operator on a smooth manifold,one may be interested in diagonalising it by choosing eigenvectors of its principal symbol in a smooth manner. We show that diagonalisation is not always possible, on the whole cotangent bundle or even in a single fibre. We identify global and local topological obstructions to diagonalisation and examine physically meaningful examples demonstrating that all possible scenarios can occur.

AB - Given a matrix pseudodifferential operator on a smooth manifold,one may be interested in diagonalising it by choosing eigenvectors of its principal symbol in a smooth manner. We show that diagonalisation is not always possible, on the whole cotangent bundle or even in a single fibre. We identify global and local topological obstructions to diagonalisation and examine physically meaningful examples demonstrating that all possible scenarios can occur.

KW - math.AP

KW - math-ph

KW - math.MP

KW - primary 58J40, secondary 35G35, 35J46, 35J47, 35J48

UR - http://www.scopus.com/inward/record.url?scp=85144950277&partnerID=8YFLogxK

U2 - 10.1090/bproc/147

DO - 10.1090/bproc/147

M3 - Article

SN - 2330-1511

VL - 9

SP - 472

EP - 486

JO - Proceedings of the American Mathematical Society: Series B

JF - Proceedings of the American Mathematical Society: Series B

IS - 43

ER -

Topological obstructions to the diagonalisation of pseudodifferential systems

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this