# Maximal and minimal operators

From Encyclopedia of Mathematics

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.

#### References

[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: http://encyclopediaofmath.org/index.php?title=Maximal_and_minimal_operators&oldid=11405

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098