Maximal and minimal operators

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The maximal and minimal extensions of an operator defined by a given differential expression on the subspace of functions of compact support. The domains of definition of the maximal and minimal operators can be concretely described in a number of cases, for example, for an ordinary differential operator, for elliptic operators and for differential operators with constant coefficients.


[1] Yu.M. [Yu.M. Berezanskii] Berezanskiy, "Expansion in eigenfunctions of selfadjoint operators" , Amer. Math. Soc. (1968) (Translated from Russian)
How to Cite This Entry:
Maximal and minimal operators. A.I. LoginovV.S. Shul'man (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098