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 Eurasian Math. J., 2014, Volume 5, Number 2, Pages 132–138 (Mi emj160)

Short communications

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

V. I. Burenkovab, T. V. Tararykovaba

a Faculty of Mechanics and Mathematics, L. N. Gumilyov Eurasian National University, 2 Mirzoyan St., 010008 Astana, Kazakhstan
b Cardiff School of Mathematics, Cardiff University, Senghennydd Rd. CF24 4AG Cardiff, UK

Abstract: An explicit formula is presented for the norm if $1\le p\le\infty$ and for the quasi-norm if $0<p<1$ of a linear vector-functional $L\colon H\to l_p$ 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.

Keywords and phrases: continuous linear vector-functional, Riesz theorem, extremal elements, Euler's equation, nonlinear eigenvalue problem.

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MSC: 46C99, 47A75
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Citation: V. I. Burenkov, T. V. Tararykova, “On the spectrum of a nonlinear operator associated with calculation of the norm of a linear vector-functional”, Eurasian Math. J., 5:2 (2014), 132–138

Citation in format AMSBIB
\Bibitem{BurTar14} \by V.~I.~Burenkov, T.~V.~Tararykova \paper On the spectrum of a~nonlinear operator associated with calculation of the norm of a~linear vector-functional \jour Eurasian Math. J. \yr 2014 \vol 5 \issue 2 \pages 132--138 \mathnet{http://mi.mathnet.ru/emj160}