Accretive and nonnegative perturbations of an abstract analogy for the operator of the third boundary problem and corresponding variational problems

Author H. M. Kachurivska, O. G. Storozh
a.kachurivska@mail.ru, storog@ukr.net
i i i, i i i ii I

Abstract In the paper the role of initial object is played by the positively definite operator L0 acting in a Hilbert space H. The main object of the investigation is operator L~ B: It is interpreted as a perturbation of some proper extension of L0. Using methods of the extension theory the criteria of maximal accretivity and maximal nonnegativity for L~ B are established. In the case when L~ B is a positively definite operator, its energetic space is constructed and the solvability of corresponding variational problem is proved. Moreover, the situation when L0 is minimal differential operator generated in the space of infinite-dimensional vector-functions by the Sturm-Liouville differential expression is considered.
Keywords Hilbert space; operator; nonnegative; extension
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Pages 201-212
Volume 36
Issue 2
Year 2011
Journal Matematychni Studii
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