Minimality of derivative chains,corresponding to a boundary value problem on a finite segment |
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Authors: | G V Radzievskii |
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Institution: | (1) Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, Kiev |
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Abstract: | One investigates the minimality of derivative chains, constructed from the root vectors of polynomial pencils of operators, acting in a Hilbert space. One investigates in detail the quadratic pencil of operators. In particular, for L()=L0+L1+2L2 with bounded operators L00, L20 and Re L10, one shows the minimality in the space173-02 of the system {xk, kekxk}, where xk are eigenvectors of L(), corresponding to the characteristic numbers kin the deleted neighborhoods of which one has the representation L–1()=(–k)–1RK+WK() with one-dimensional operators Rk and operator-valued functions WK(), k=1, 2, ..., analytic for =k.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 2, pp. 195–205, February, 1990. |
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