Isotropic functions revisited

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:	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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