Let L 0 be a densely defined minimal linear operator in a Hilbert space H. We prove theorem that if there exists at least one correct extension L S of L 0 with the property D(L S ) = D(L * S ), then we can describe all correct extensions L with the property D(L) = D(L * ). We also prove that if L 0 is formally normal and there exists at least one correct normal extension L N , then we can describe all correct normal extensions L of L 0 . As an example, the Cauchy-Riemann operator is given.
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