On the spectrum of a nonlinear operator associated with calculation of the norm of a linear vector-functional.

Burenkov, Victor and Tararykova, Tamara 2014. On the spectrum of a nonlinear operator associated with calculation of the norm of a linear vector-functional. Eurasian Mathematical Journal 5 (2) , pp. 132-138.

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Abstract

An explicit formula is presented for the norm if 1 ≤ p ≤ ∞ and for the quasi-norm if 0 < p < 1 of a linear vector-functional L : H → lp on a Hilbert space H and the set of all extremal elements is described. All eigenvalues and eigenvectors of a nonlinear homogeneous operator entering the corresponding Euler’s equation, are written out explicitly.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Continuous linear vector-functional, Riesz Theorem, extremal elements, Euler’s equation, nonlinear eigenvalue problem
Publisher:	L. N. Gumilyov Eurasian National University
ISSN:	2077-9879
Date of First Compliant Deposit:	30 March 2016
Date of Acceptance:	23 May 2014
Last Modified:	23 May 2023 14:13
URI:	https://orca.cardiff.ac.uk/id/eprint/81988

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