Mathematics and Statistics Vol. 9(2), pp. 179 - 187
DOI: 10.13189/ms.2021.090213
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A Dirac Delta Operator

Juan Carlos Ferrando ^*
Centro de Investigacion Operativa, Universidad Miguel Hernandez, E-03202 Elche, Spain

ABSTRACT

If T is a (densely defined) self-adjoint operator acting on a complex Hilbert space H and I stands for the identity operator, we introduce the delta function operator at T. When T is a bounded operator, then is an operator-valued distribution. If T is unbounded, is a more general object that still retains some properties of distributions. We provide an explicit representation of in some particular cases, derive various operative formulas involving and give several applications of its usage in Spectral Theory as well as in Quantum Mechanics.

KEYWORDS
Hilbert Space, Self-adjoint Operator, Vectorvalued Distribution, Spectral Measure

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Juan Carlos Ferrando , "A Dirac Delta Operator," Mathematics and Statistics, Vol. 9, No. 2, pp. 179 - 187, 2021. DOI: 10.13189/ms.2021.090213.

(b). APA Format:
Juan Carlos Ferrando (2021). A Dirac Delta Operator. Mathematics and Statistics, 9(2), 179 - 187. DOI: 10.13189/ms.2021.090213.