Let h be a Hilbert space and let A be a symmetric operator in h with arbitrary (not necessarily equal) deficiency indices <$E n sub symbol С (A)>. We introduce a new concept of a D-boundary triplet for <$E A sup *>, which may be considered as a natural generalization of the known concept of a boundary triplet (boundary value space) for an operator with equal deficiency indices. With a D-triplet for <$E A sup *> we associate two Weyl functions <$E M sub + ( cdot )> and <$E M sub - ( cdot )>. It is proved that the functions <$E M sub symbol С ( cdot )> posses a number of properties similar to those of the known Weyl functions (Q-functions) for the case <$E n sub + (A)~=~n sub - (A)>. We show that every D-triplet for <$E A sup *> gives rise to Krein type formulas for generalized resolvents of the operator A with arbitrary deficiency indices. The resolvent formulas describe the set of all generalized resolvents by means of two pairs of operator functions which belongs to the Nevanlinna type class <$E R Tilde~(H sub 0 ,~H sub 1 )>. This class has been earlier introduced by the author.

Індекс рубрикатора НБУВ: В162.4

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Оператори у гільбертовому просторі

Шифр НБУВ: Ж41243 Пошук видання у каталогах НБУВ 

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