Let $A_{0}$
be a closed,
minimal symmetric operator from a Hilbert space $\mathbb{H}$
into
$\mathbb{H}$ with domain not dense in $\mathbb{H}$ . Let
$\widehat{A}$
also be a correct selfadjoint extension of $A_{0}$ .
The purpose of this paper is (1) to characterize, with the help of
$\widehat{A}$ , all the correct selfadjoint extensions $B$ of
$A_{0}$ with domain equal to $\hmmathcheck{D}(\widehat{A})$ , (2)
to give the solution of their corresponding problems, (3) to find
sufficient conditions for $B$
to be positive (definite) when
$\widehat{A}$ is positive (definite).