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


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Authors

  • Victor Ivanovich Burenkov
  • Tamara Vasil’evna Tararykova

Keywords:

continuous linear vector-functional, Riesz Theorem, extremal elements, Euler’s equation, nonlinear eigenvalue problem

Abstract

An explicit formula is presented for the norm if \( 1 \leq p \leq \infty \) and for the quasi-norm if \( 0 < p < 1 \) of a linear vector-functional \( L : H \rightarrow \ell_p \) 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.

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Published

2014-06-30

How to Cite

Burenkov, V. I., & Tararykova, T. V. (2014). On the spectrum of a nonlinear operator associated with calculation of the norm of a linear vector-functional. Eurasian Mathematical Journal, 5(2), 132–138. Retrieved from https://emj.enu.kz/index.php/main/article/view/575

Issue

Vol. 5 No. 2 (2014)

Section

Articles