Minimality of root vectors of operator functions analytic in an angle |
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Authors: | G. V. Radzievskii |
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Affiliation: | (1) Institute of Mathematics, Ukrainian Academy of Sciences, Kiev |
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Abstract: | We study the minimality of elementsxh,j,k of canonical systems of root vectors. These systems correspond to the characteristic numbers k of operator functionsL() analytic in an angle; we assume that operators act in a Hilbert space. In particular, we consider the case whereL()=I+T()c, >0,I is an identity operator,C is a completely continuous operator, (I- C)–1c for ¦arg¦, 0<<, the operator functionT() is analytic, and T()c for ¦arg¦<. It is proved that, in this case, there exists >0 such that the system of vectorsCvxh,j,k is minimal in for arbitrary positive <1+, provided that ¦k¦>.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 5, pp. 545–566, May, 1994.This research was partially supported by the Ukrainian State Committee of Science and Technology. |
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