Semiclassical analysis of a nonlocal boundary value problem related to magnitude
(2023) In Journal d'Analyse Mathematique- Abstract
We study a Dirichlet boundary problem related to the fractional Laplacian in a manifold. Its variational formulation arises in the study of magnitude, an invariant of compact metric spaces given by the reciprocal of the ground state energy. Using recent techniques developed for pseudodifferential boundary problems we discuss the structure of the solution operator and resulting properties of the magnitude. In a semiclassical limit we obtain an asymptotic expansion of the magnitude in terms of curvature invariants of the manifold and the boundary, similar to the invariants arising in short-time expansions for heat kernels.
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https://lup.lub.lu.se/record/823c6170-e16c-481f-aef0-95a430e6df4d
- author
- Gimperlein, Heiko ; Goffeng, Magnus LU and Louca, Nikoletta
- organization
- publishing date
- 2023
- type
- Contribution to journal
- publication status
- epub
- subject
- in
- Journal d'Analyse Mathematique
- publisher
- Magnes Press
- external identifiers
-
- scopus:85180170092
- ISSN
- 0021-7670
- DOI
- 10.1007/s11854-023-0310-3
- language
- English
- LU publication?
- yes
- id
- 823c6170-e16c-481f-aef0-95a430e6df4d
- date added to LUP
- 2024-01-10 10:06:18
- date last changed
- 2024-01-10 10:08:07
@article{823c6170-e16c-481f-aef0-95a430e6df4d,
abstract = {{<p>We study a Dirichlet boundary problem related to the fractional Laplacian in a manifold. Its variational formulation arises in the study of magnitude, an invariant of compact metric spaces given by the reciprocal of the ground state energy. Using recent techniques developed for pseudodifferential boundary problems we discuss the structure of the solution operator and resulting properties of the magnitude. In a semiclassical limit we obtain an asymptotic expansion of the magnitude in terms of curvature invariants of the manifold and the boundary, similar to the invariants arising in short-time expansions for heat kernels.</p>}},
author = {{Gimperlein, Heiko and Goffeng, Magnus and Louca, Nikoletta}},
issn = {{0021-7670}},
language = {{eng}},
publisher = {{Magnes Press}},
series = {{Journal d'Analyse Mathematique}},
title = {{Semiclassical analysis of a nonlocal boundary value problem related to magnitude}},
url = {{http://dx.doi.org/10.1007/s11854-023-0310-3}},
doi = {{10.1007/s11854-023-0310-3}},
year = {{2023}},
}