Distribution theory for discontinuous test functions and differential operators with generalized coefficients
(1996) In Journal of Mathematical Analysis and Applications 201(1). p.287323 Abstract
 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 fourparameter family of Schrodinger 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.... (More)
 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 fourparameter family of Schrodinger 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. (C) 1996 Academic Press, Inc. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/758068
 author
 Kurasov, Pavel ^{LU}
 organization
 publishing date
 1996
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 POINT INTERACTIONS, ONEDIMENSION
 in
 Journal of Mathematical Analysis and Applications
 volume
 201
 issue
 1
 pages
 287  323
 publisher
 Elsevier
 external identifiers

 Scopus:0030187273
 ISSN
 0022247X
 DOI
 10.1006/jmaa.1996.0256
 language
 English
 LU publication?
 yes
 id
 8d21f46af31543daa5a7f0962302aedf (old id 758068)
 alternative location
 http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6WK245MFXXV1G1&_cdi=6894&_user=745831&_orig=search&_coverDate=07%2F01%2F1996&_sk=997989998&view=c&wchp=dGLzVlzzSkzk&md5=ac8b76b8e95cf2f3393fb062b2734d7c&ie=/sdarticle.pdf
 date added to LUP
 20080901 16:11:39
 date last changed
 20161204 04:37:11
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