Basics of the Theory of Self-adjoint Extensions of Symmetric Operators

Abstract

AbstractWe remind the reader of the basics of the general theory of self-adjoint extensions of unbounded symmetric operators. The exposition is based on a notion of asymmetry forms of the adjoint operator. The principal statements concerning the possibility and specification of self-adjoint extensions both in terms of isometries between the deficient subspaces and in terms of the asymmetry forms are collected in the main theorem, followed by a comment on a direct application of the main theorem to physical problems of quantization.KeywordsAdjoint OperatorSymmetric OperatorIsometric MappingSymmetric ExtensionIsometric OperatorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.