Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Regularity properties of distributions and ultradistributions


Authors: S. Pilipovic and D. Scarpalezos
Journal: Proc. Amer. Math. Soc. 129 (2001), 3531-3537
MSC (2000): Primary 46F05, 46F30, 03C20
Published electronically: June 28, 2001
MathSciNet review: 1860484
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract:

We give necessary and sufficient conditions for a regularized net of a distribution in an open set $\Omega$which imply that it is a smooth function or $C^k$ function in $\Omega$. We also give necessary and sufficient conditions for an ultradistribution to be an ultradifferentiable function of corresponding class.


References [Enhancements On Off] (What's this?)

  • 1. Hebe A. Biagioni, A nonlinear theory of generalized functions, 2nd ed., Lecture Notes in Mathematics, vol. 1421, Springer-Verlag, Berlin, 1990. MR 1049623
  • 2. Jean-François Colombeau, New generalized functions and multiplication of distributions, North-Holland Mathematics Studies, vol. 84, North-Holland Publishing Co., Amsterdam, 1984. Notas de Matemática [Mathematical Notes], 90. MR 738781
  • 3. Yu. V. Egorov, On the theory of generalized functions, Uspekhi Mat. Nauk 45 (1990), no. 5(275), 3–40, 222 (Russian); English transl., Russian Math. Surveys 45 (1990), no. 5, 1–49. MR 1084986, 10.1070/RM1990v045n05ABEH002683
  • 4. Ricardo Estrada and Ram P. Kanwal, Asymptotic analysis, Birkhäuser Boston, Inc., Boston, MA, 1994. A distributional approach. MR 1254657
  • 5. Lars Hörmander, The analysis of linear partial differential operators. I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 256, Springer-Verlag, Berlin, 1983. Distribution theory and Fourier analysis. MR 717035
  • 6. Hikosaburo Komatsu, Ultradistributions. III. Vector-valued ultradistributions and the theory of kernels, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 29 (1982), no. 3, 653–717. MR 687595
  • 7. H. Komatsu, Microlocal Analysis in Gevrey Classes and in Convex Domains, Springer, Lec. Not. Math. 1726(1989), 426 - 493.
  • 8. M. Oberguggenberger, Multiplication of distributions and applications to partial differential equations, Pitman Research Notes in Mathematics Series, vol. 259, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1992. MR 1187755
  • 9. Hans-Joachim Petzsche, Generalized functions and the boundary values of holomorphic functions, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 31 (1984), no. 2, 391–431. MR 763428
  • 10. Stevan Pilipović, Microlocal analysis of ultradistributions, Proc. Amer. Math. Soc. 126 (1998), no. 1, 105–113. MR 1451826, 10.1090/S0002-9939-98-04357-3
  • 11. S. Pilipovic, D. Scarpalezos, Colombeau Generalized Ultradistributions, Math. Proc. Camb. Phil. Soc., 130(2001), 541-553. CMP 2001:09

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46F05, 46F30, 03C20

Retrieve articles in all journals with MSC (2000): 46F05, 46F30, 03C20


Additional Information

S. Pilipovic
Affiliation: Institute of Mathematics, University of Novi Sad, Trg D.Obradovića 4, 21000 Novi Sad, Yugoslavia

D. Scarpalezos
Affiliation: U.F.R. de Mathématiques, Universite Paris 7, 2 place Jussieu, Paris 5$\buildrel e \over{}$, 75005, France

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06013-0
Received by editor(s): February 21, 2000
Published electronically: June 28, 2001
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2001 American Mathematical Society