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Integral Transforms and Special Functions Volume 22, 2011 - Issue 4-5: THE INTERNATIONAL CONFERENCE ON GENERALIZED FUNCTIONS GF 2009, VIENNA, 31 AUGUST–4 SEPTEMBER 2009
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Original Articles

An axiomatic approach to the non-linear theory of generalized functions and consistency of Laplace transforms

Todor D. Todorov Mathematics Department, California Polytechnic State University, San Luis Obispo, CA, 93407, USACorrespondence[email protected]
Pages 367-374 | Received 20 Jan 2010, Published online: 17 May 2011

References

  • Colombeau , J. F. 1984 . New generalized functions and multiplication of distributions . North-Holland Math. Stud. , 84 : 135 – 148 .
  • Hahn , H. 1907 . Über die nichtarchimedischen Grössensysteme . Sitz. K. Akad. Wiss. , 116 : 601 – 655 .
  • Kaneko , A. 1988 . Introduction to Hyperfunctions , Dordrecht/Boston : Kluwer .
  • Kaplansky , I. 1942 . Maximal fields with valuations . Duke Math. J. , 9 : 303 – 321 .
  • Krull , W. 1932 . Allgemeine Bewertungstheorie . J. Reine Angew. Math. , 167 : 160 – 196 .
  • Levi-Civita , T. 1954 . Sugli Infiniti ed Infinitesimi Attuali Quali Elementi Analitici . Opere Mathematiche , 1 : 1 – 39 . (1892–1893)
  • Lightstone , A. H. and Robinson , A. 1975 . “ Nonarchimedean Fields and Asymptotic Expansions ” . North-Holland, Amsterdam
  • Luxemburg , W. A.J. 1976 . On a class of valuation fields introduced by Robinson . Israel J. Math. , 25 : 189 – 201 .
  • Oberguggenberger , M. and Todorov , T. 1998 . An embedding of Schwartz distributions in the algebra of asymptotic functions . Int. J. Math. Math. Sci. , 21 : 417 – 428 .
  • Oberguggenberger , M. and Vernaeve , H. 2008 . Internal sets and internal functions in Colombeau theory . J. Math. Anal. Appl. , 341 ( 1 ) : 649 – 659 .
  • Todorov , T. and Wolf , R. 2004 . “ Hahn field representation of A. Robinson's asymptotic numbers ” . In Nonlinear Algebraic Analysis and Applications, Proceedings of the ICGF 2000 , Edited by: Delcroix , A. , Hasler , M. , Marti , J.-A. and Valmorin , V. 357 – 374 . Cottenham, Cambridge : Cambridge Scientific Publishers . Available at arXiv:math/0601722v1 [math.AC]
  • Todorov , T. and Vernaeve , H. 2008 . Full algebra of generalized functions and non-standard asymptotic analysis . Logic Anal. , 1 ( 3 ) : 205 – 234 .
  • van der Waerden , B. L. 1966 . “ Algebra ” . In , 7 , Vol. 1 , Berlin : Springer .
  • Vladimirov , V. 1979 . “ Generalized Functions in Mathematical Physics ” . Moscow : Mir-Publisher .
  • Zariski , O. and Samuel , P. 1975 . “ Commutative Algebra ” . Vol. II , New York, Heidelberg, Berlin : Springer .

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