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Distribution theory for discontinuous test functions and differential operators with generalized coefficients

Kurasov, Pavel LU (1996) In Journal of Mathematical Analysis and Applications 201(1). p.287-323
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 four-parameter 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 four-parameter 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)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
POINT INTERACTIONS, ONE-DIMENSION
in
Journal of Mathematical Analysis and Applications
volume
201
issue
1
pages
287 - 323
publisher
Elsevier
external identifiers
  • Scopus:0030187273
ISSN
0022-247X
DOI
10.1006/jmaa.1996.0256
language
English
LU publication?
yes
id
8d21f46a-f315-43da-a5a7-f0962302aedf (old id 758068)
alternative location
http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6WK2-45MFXXV-1G-1&_cdi=6894&_user=745831&_orig=search&_coverDate=07%2F01%2F1996&_sk=997989998&view=c&wchp=dGLzVlz-zSkzk&md5=ac8b76b8e95cf2f3393fb062b2734d7c&ie=/sdarticle.pdf
date added to LUP
2008-09-01 16:11:39
date last changed
2016-12-04 04:37:11
@misc{8d21f46a-f315-43da-a5a7-f0962302aedf,
  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 four-parameter 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.},
  author       = {Kurasov, Pavel},
  issn         = {0022-247X},
  keyword      = {POINT INTERACTIONS,ONE-DIMENSION},
  language     = {eng},
  number       = {1},
  pages        = {287--323},
  publisher    = {ARRAY(0x8ccba58)},
  series       = {Journal of Mathematical Analysis and Applications},
  title        = {Distribution theory for discontinuous test functions and differential operators with generalized coefficients},
  url          = {http://dx.doi.org/10.1006/jmaa.1996.0256},
  volume       = {201},
  year         = {1996},
}