Theoretical and Mathematical Physics

, Volume 102, Issue 2, pp 133–143 | Cite as

Commutative properties of singularly perturbed operators

  • N. E. Dudkin
  • V. D. Koshmanenko


Suppose the self-adjoint operatorA in the Hilbert spaceH commutes with the bounded operatorS. Suppose another self-adjoint operatorĀ is singularly perturbed with respect toA, i.e., it is identical toA on a certain dense set inH. We study the following question: Under what conditions doesĀ also commute withS? In addition, we consider the case whenS is unbounded and also the case whenS is replaced by a singularly perturbed operator S. As application, we consider the Laplacian inL2(R q ) that is singularly perturbed by a set of δ functions and commutes with the symmetrization operator inR q ,q=2, 3, or with regular representations of arbitrary isometric transformations inR q ,q≤3.


Symmetrization Operator Regular Representation Commutative Property Isometric Transformation Hilbert spaceH 


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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • N. E. Dudkin
  • V. D. Koshmanenko

There are no affiliations available

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