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An evaluation of powers of the negative spectrum of Schrödinger operator equation with a singularity at zero. (English) Zbl 1378.34082
Summary: In this study, we investigate the discreteness and finiteness of the negative spectrum of the differential operator $$L$$ in the Hilbert space $$L_{2} (H, [0,\infty))$$, defined by $Ly=- \frac{d^{2} y}{d x^{2}} + \frac{A(A+I)}{x^{2}} y-Q(x)y$ under the boundary condition $$y (0) =0$$.
In the case when the negative spectrum is finite, we obtain an evaluation for the sums of powers of the absolute values of negative eigenvalues. The obtained result is applied to a class of equations of mathematical physics.
MSC:
 34G10 Linear differential equations in abstract spaces 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) 34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
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