### Integrable systems via inverse integrating factor.

J. Chavarriga, J. Giné (1998)

Extracta Mathematicae

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J. Chavarriga, J. Giné (1998)

Extracta Mathematicae

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M. S. A. C. Castilla, Vinicio Moauro, Piero Negrini, Waldyr Muniz Oliva (1993)

Annales de l'I.H.P. Physique théorique

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Shibata, Tetsutaro (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Lorenza Diomeda, Benedetta Lisena (1987)

Rendiconti del Seminario Matematico della Università di Padova

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Ryszard Szwarc (1998)

Colloquium Mathematicae

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Harper’s operator is defined on ${\ell}^{2}\left(Z\right)$ by $${H}_{\theta}\xi \left(n\right)=\xi (n+1)+\xi (n-1)+2cosn\theta \phantom{\rule{0.166667em}{0ex}}\xi \left(n\right),$$ where $\theta \phantom{\rule{-0.166667em}{0ex}}\in \phantom{\rule{-0.166667em}{0ex}}[0,\pi ]$. We show that the norm of $\parallel {H}_{\theta}\parallel $ is less than or equal to $2\sqrt{2}$ for $\pi /2\le \theta \le \pi $. This solves a conjecture stated in [1]. A general formula for estimating the norm of self-adjoint tridiagonal infinite matrices is also derived.

Ľudmila Zajacová (1986)

Mathematica Slovaca

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Ioan Serb (2001)

Collectanea Mathematica

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Variants of Khintchine's inequality with coefficients depending on the vector dimension are proved. Equality is attained for different types of extremal vectors. The Schur convexity of certain attached functions and direct estimates in terms of the Haagerup type of functions are also used.