Sunto
Delineiamo una dimostrazione, usando metodi della teoria degli operatori, del fatto che un operatore limitato in
, 1<p<∞, commuta con l’operatore di Laplace −d 2/dx 2 se e solo se è della formaU+RV, doveR è l’operatore riflessione in
eU eV sono operatorip-moltiplicatori. Suggeriamo inoltre alcune conseguenze del metodo dimostrativo.
Summary
We outline an operator theoretic proof of the fact that a bounded operator in
, 1<p<∞, commutes with the Laplace operator −d 2/dx 2 if, and only if, it is of the formU+RV whereR is the reflection operator in
andU. V arep-multiplier operators. Some consequences of this method of proof are also suggested.
This is a preview of subscription content, log in via an institution to check access.
Bibliography
Dunford N. andSchwartz J. T.,Linear operators II: Spectral theory of self-adjoint operators in Hilbert space, Interscience Publ., New York, 1963.
Greiner G., Remarks concerning the eigenvalues of the Laplace operator,Semesterbericht Funktionalysis Tübingen, Vol. 13, Wintersemester 87/88, p. 97–105.
Kluvánek I., Scalar operators and integration,J. Austral. Math. Soc. (Series A), (to appear).
Ricker W., The commutant of the Laplace operator in
, Math. Nachr. (to appear).Ricker W., AnL 1-type functional calculus for the Laplace operator in
, J. Operator Theory, (to appear).
, Math. Nachr. (to appear).
, J. Operator Theory, (to appear).Author information
Authors and Affiliations
Additional information
(Conferenza tenuta il 19 novembre 1897)
Rights and permissions
About this article
Cite this article
Ricker, W.J. Spectral projections and the commutant of the Laplace operator in
.
Seminario Mat. e. Fis. di Milano 57, 519–528 (1987). https://doi.org/10.1007/BF02925068
Issue Date:
DOI: https://doi.org/10.1007/BF02925068