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

  • D. M. Gitman
  • I. V. Tyutin
  • B. L. Voronov
Part of the Progress in Mathematical Physics book series (PMP, volume 62)


We 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.


Adjoint Operator Symmetric Operator Isometric Mapping Symmetric Extension Isometric Operator 
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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • D. M. Gitman
    • 1
  • I. V. Tyutin
    • 2
  • B. L. Voronov
    • 2
  1. 1.Instituto de FísicaUniversidade de São PauloSão PauloBrasil
  2. 2.Department of Theoretical PhysicsP.N. Lebedev Physical InstituteMoscowRussia

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