Investigation of the dimension of the spectral projection of a self-adjoint second order quasidifferential operator

M. Yu. Vatolkin

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2024), pp. 47-62

Résumé

Let $\lambda_1$ and $\lambda_2$ be real, $\lambda_1<\lambda_2,$ functions $\psi_{-}(\lambda_i,t)$ be solutions to the second order quasidifferential equations $L\psi_-={\lambda_i }_P^0\psi_-$, $i=1,2$, satisfying a homogeneous boundary condition at point $a.$ We express the number of eigenvalues of operator $L,$ belonging to the interval $(\lambda_1,\lambda_2)$ (or the dimension of its spectral projection relative to the interval $(\lambda_1,\lambda_2)$), in terms of the number of zeros of the Vronskian composed for the functions $\psi_{-}(\lambda_1,t)$ and $\psi_{-}(\lambda_2,t).$

Détail

Keywords: quasidifferential operator, spectral projection, self-adjoint quasidifferential expression.

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