Remark to the comparison of solution properties of Love's equation with those of wave equation

Věra Radochová

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Harper’s operator is defined on $ℓ^{2} (Z)$ by $H_{θ} ξ (n) = ξ (n + 1) + ξ (n - 1) + 2 cos n θ ξ (n),$ where $θ \in [0, π]$ . We show that the norm of $∥ H_{θ} ∥$ is less than or equal to $2 \sqrt{2}$ for $π / 2 \leq θ \leq π$ . This solves a conjecture stated in [1]. A general formula for estimating the norm of self-adjoint tridiagonal infinite matrices is also derived.

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