Geodesic
Self-adjoint quadratic bundles
Izvestiya. Mathematics , Tome 3 (1969) no. 1, pp. 131-145

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The present article contains a study of the properties of the self-adjoint quadratic bundle $$ Q(\lambda)=\lambda^2{I}+\lambda B+C $$ and the associated quadratic operator equation $$ Z^2+BZ+C=0. $$ The theorems obtained are applied to a number of problems in mathematical physics. 
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     author = {E. A. Larionov},
     title = {Self-adjoint quadratic bundles},
     journal = {Izvestiya. Mathematics },
     pages = {131--145},
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     volume = {3},
     number = {1},
     year = {1969},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1969_3_1_a8/}
}
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E. A. Larionov. Self-adjoint quadratic bundles. Izvestiya. Mathematics , Tome 3 (1969) no. 1, pp. 131-145. http://geodesic.mathdoc.fr/item/IM2_1969_3_1_a8/