Abstract:
In this paper there is considered the description of all well-defined restrictions of a maximal operator in a Hilbert space. A class of well-defined restrictions is found for which a similar transformation has the domain of the fixed well-defined restriction. The resulting theorem is applied
to the study of $n$-order differentiation operator and the Laplace operator.
Keywords and phrases:maximal (minimal) operator, well-defined restriction, well-defined extension, similar operators, singular coefficients, Riesz basis with brackets.
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