Equivalence of certain principal vectors of polynomial operator sheaves |
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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: | The equivalence of derived chains constructed from the principal vectors of polynomial sheafs of operators acting in Hilbert space is studied. These derived chains correspond to different boundary-value problems on the semi-axis for operator-differential equations whose symbol is these operator sheafs. On the basis of equivalence tests assertions are deduced concerning the minimality of derived chains corresponding to a boundary-value problem on the semi-axis in the case in which the initial conditions of the vector solution at zero are known, and the solution itself obeys radiation-type conditions at infinity.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 7, pp. 948–970, July, 1992. |
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