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Minimality of derivative chains, corresponding to a boundary value problem on a finite segment

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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(λ)=L0+λL1+λ2L2 with bounded operators L0≥0, L2≤0 and Re L1≥0, one shows the minimality in the space173-02 of the system {xk, μkeμkxk}, where xk are eigenvectors of L(λ), corresponding to the characteristic numbers μkin the deleted neighborhoods of which one has the representation L−1(λ)=(λ−μk)−1RK+WK(λ) with one-dimensional operators Rk and operator-valued functions WK(λ), k=1, 2, ..., analytic for λ=μk.

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Literature cited

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, Kiev

    G. V. Radzievskii

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  1. G. V. Radzievskii
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 2, pp. 195–205, February, 1990.

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Radzievskii, G.V. Minimality of derivative chains, corresponding to a boundary value problem on a finite segment. Ukr Math J 42, 173–182 (1990). https://doi.org/10.1007/BF01071011

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  • DOI: https://doi.org/10.1007/BF01071011

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