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Distribution theory for discontinuous test functions and differential operators with generalized coefficients
Luleå tekniska universitet.
1996 (English)In: Banach Journal of Mathematical Analysis, ISSN 1735-8787, Vol. 201, no 1, p. 297-323Article in journal (Refereed) Published
Abstract [en]

Investigation of the differential operators with the generalized coefficients having singular support on a disjoint set of points requires the consideration of the distribution theory with the set of discontinuous test functions. Such a distribution theory for test functions having discontinuity at one point is developed. A four-parameter family of Schrödinger operators, formed by the operators with singular potential, singular metrics and singular gauge field, is considered. It is proved that this family of singular interactions describes all possible selfadjoint extensions of the second derivative operator defined on the functions vanishing in a neighbourhood of the point. Approximation by operators with smooth coefficients is discussed.

Place, publisher, year, edition, pages
1996. Vol. 201, no 1, p. 297-323
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-3401DOI: 10.1006/jmaa.1996.0256Local ID: 13a98210-e22b-11dd-981b-000ea68e967bOAI: oai:DiVA.org:ltu-3401DiVA: diva2:976259
Note
Godkänd; 1996; 20090114 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-21Bibliographically approved

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