Distribution theory for discontinuous test functions and differential operators with generalized coefficients
(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)
Please use this url to cite or link to this publication:
https://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, 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
- 2016-04-04 09:05:34
- date last changed
- 2022-03-15 17:37:54
@article{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}},
keywords = {{POINT INTERACTIONS; ONE-DIMENSION}},
language = {{eng}},
number = {{1}},
pages = {{287--323}},
publisher = {{Elsevier}},
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}},
doi = {{10.1006/jmaa.1996.0256}},
volume = {{201}},
year = {{1996}},
}