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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1975, Volume 18, Issue 1, Pages 3–7 (Mi mz7618)

Self-adjointness of the dirac operator in a space of vector functions

V. A. Bezverkhnii

M. V. Lomonosov Moscow State University

Abstract: This paper is devoted to the proof of the self-adjointness of the minimal operator defined on the space $L_2(-\infty,\infty;H)$ ($H$ being a separable Hilbert space) by the expression $l=iJ\frac d{dt}+A+B(t)$. The coefficients in this expression are self-adjoint operators on $H$, with $A$ being unbounded, $AJ+JA=0$, and the function $\|B(t)\|_H$ being assumed to lie in $L_2^{\operatorname{loc}}(-\infty,\infty)$. The result obtained is applicable to the Dirac operator.

Full text: PDF file (297 kB)

English version:
Mathematical Notes, 1975, 18:1, 583–585

Bibliographic databases:

UDC: 517

Citation: V. A. Bezverkhnii, “Self-adjointness of the dirac operator in a space of vector functions”, Mat. Zametki, 18:1 (1975), 3–7; Math. Notes, 18:1 (1975), 583–585

Citation in format AMSBIB
\Bibitem{Bez75} \by V.~A.~Bezverkhnii \paper Self-adjointness of the dirac operator in a~space of vector functions \jour Mat. Zametki \yr 1975 \vol 18 \issue 1 \pages 3--7 \mathnet{http://mi.mathnet.ru/mz7618} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=390826} \zmath{https://zbmath.org/?q=an:0316.47019} \transl \jour Math. Notes \yr 1975 \vol 18 \issue 1 \pages 583--585 \crossref{https://doi.org/10.1007/BF01461134}