Geodesic
On symmetrizable operators of which some iteration satisfies a positive definite condition
Matematičeskie zametki, Tome 5 (1969) no. 1, pp. 71-76 Cet article a éte moissonné depuis la source Math-Net.Ru

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Considered are linear (in general, unbounded) operators $A$, defined on a set $R$ which is dense in the Hilbert Space $X$, which are symmetrizable by a symmetric operator $H$ in $R$. Under the condition that there exists an integer $p\ge0$ for which $(HA^px,x)\ge0$ for any $x\in R$, the spectral properties of the operator $A$ and the solutions of the equation $x-\lambda Ax=y,~x,y\in R$ are investigated. The results obtained are applied to investigating some boundary-value problems for differential equations. 
@article{MZM_1969_5_1_a8,
     author = {D. F. Kharazov},
     title = {On symmetrizable operators of which some iteration satisfies a~positive definite condition},
     journal = {Matemati\v{c}eskie zametki},
     pages = {71--76},
     year = {1969},
     volume = {5},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_5_1_a8/}
}
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D. F. Kharazov. On symmetrizable operators of which some iteration satisfies a positive definite condition. Matematičeskie zametki, Tome 5 (1969) no. 1, pp. 71-76. http://geodesic.mathdoc.fr/item/MZM_1969_5_1_a8/