On Generalized Models and Singular Products of Distributions in Colombeau Algebra G(R)

Damyanov, Blagovest P.

Mathematica Balkanica New Series (2013)

  • Volume: 27, Issue: 1-2, page 21-33
  • ISSN: 0205-3217

Abstract

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MSC 2010: 46F30, 46F10Modelling of singularities given by discontinuous functions or distributions by means of generalized functions has proved useful in many problems posed by physical phenomena. We introduce in a systematic way generalized functions of Colombeau that model such singularities. Moreover, we evaluate some products of singularity-modelling generalized functions whenever the result admits an associated distribution.

How to cite

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Damyanov, Blagovest P.. "On Generalized Models and Singular Products of Distributions in Colombeau Algebra G(R)." Mathematica Balkanica New Series 27.1-2 (2013): 21-33. <http://eudml.org/doc/281454>.

@article{Damyanov2013,
abstract = {MSC 2010: 46F30, 46F10Modelling of singularities given by discontinuous functions or distributions by means of generalized functions has proved useful in many problems posed by physical phenomena. We introduce in a systematic way generalized functions of Colombeau that model such singularities. Moreover, we evaluate some products of singularity-modelling generalized functions whenever the result admits an associated distribution.},
author = {Damyanov, Blagovest P.},
journal = {Mathematica Balkanica New Series},
keywords = {Colombeau algebra; singular products of distributions; Colombeau generalized functions; distribution spaces; singular products},
language = {eng},
number = {1-2},
pages = {21-33},
publisher = {Bulgarian Academy of Sciences - National Committee for Mathematics},
title = {On Generalized Models and Singular Products of Distributions in Colombeau Algebra G(R)},
url = {http://eudml.org/doc/281454},
volume = {27},
year = {2013},
}

TY - JOUR
AU - Damyanov, Blagovest P.
TI - On Generalized Models and Singular Products of Distributions in Colombeau Algebra G(R)
JO - Mathematica Balkanica New Series
PY - 2013
PB - Bulgarian Academy of Sciences - National Committee for Mathematics
VL - 27
IS - 1-2
SP - 21
EP - 33
AB - MSC 2010: 46F30, 46F10Modelling of singularities given by discontinuous functions or distributions by means of generalized functions has proved useful in many problems posed by physical phenomena. We introduce in a systematic way generalized functions of Colombeau that model such singularities. Moreover, we evaluate some products of singularity-modelling generalized functions whenever the result admits an associated distribution.
LA - eng
KW - Colombeau algebra; singular products of distributions; Colombeau generalized functions; distribution spaces; singular products
UR - http://eudml.org/doc/281454
ER -

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