Scheuer, Julian  ORCID: https://orcid.org/0000-0003-2664-1896
2018.
Isotropic functions revisited.
Archiv der Mathematik
110
(6)
, pp. 591-604.
10.1007/s00013-018-1162-4
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Abstract
To a real n-dimensional vector space V and a smooth, symmetric function f defined on the n-dimensional Euclidean space we assign an associated operator function F defined on linear transformations of V. F shall have the property that, for each inner product g on V, its restriction Fg to the subspace of g-selfadjoint operators is the isotropic function associated to f. This means that it acts on these operators via f acting on their eigenvalues. We generalize some well-known relations between the derivatives of f and each Fg to relations between f and F, while also providing new elementary proofs of the known results. By means of an example we show that well-known regularity properties of Fg do not carry over to F.
| Item Type: | Article |
|---|---|
| Date Type: | Publication |
| Status: | Published |
| Schools: | Schools > Mathematics |
| Publisher: | Springer Verlag (Germany) |
| ISSN: | 0003-889X |
| Date of First Compliant Deposit: | 8 October 2020 |
| Date of Acceptance: | 18 January 2018 |
| Last Modified: | 17 Nov 2024 08:15 |
| URI: | https://orca.cardiff.ac.uk/id/eprint/135462 |
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