| Title:
|
Multiplication of distributions (English) |
| Author:
|
Boie, Volker |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
2 |
| Year:
|
1998 |
| Pages:
|
309-321 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Multiplication by harmonic representations of distributions, introduced by Li Banghe, is an extension of a certain product by radial (rotationally symmetric) mollifiers and therefore a strict extension of the Kami'{n}ski and Colombeau product. (English) |
| Keyword:
|
distribution products |
| Keyword:
|
multiplication |
| Keyword:
|
harmonic representations |
| Keyword:
|
Kami'nski product |
| MSC:
|
46F10 |
| idZBL:
|
Zbl 0937.46031 |
| idMR:
|
MR1651955 |
| . |
| Date available:
|
2009-01-08T18:40:45Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119008 |
| . |
| Reference:
|
[1] Boie V.: Partielle Multiplikationen in Distributionenräumen.Dissertation, Universität Hannover, 1996. Zbl 0876.46032 |
| Reference:
|
[2] Itano M.: On the multiplicative product of distributions.J. Sci. Hiroshima Univ., Ser. A-I 29 (1965), 51-74. MR 0184079 |
| Reference:
|
[3] Jelínek J.: Distinguishing example for the Tillmann product of distributions.Comment. Math. Univ. Carolinae 31 (1990), 693-700. MR 1091366 |
| Reference:
|
[4] Jelínek J.: A contribution to the equivalence results for the product of distributions.Comment. Math. Univ. Carolinae 35 (1994), 263-266. MR 1286573 |
| Reference:
|
[5] Jelínek J.: Characterization of the Colombeau product of distributions.Comment. Math. Univ. Carolinae 27 (1986), 377-394. MR 0857556 |
| Reference:
|
[6] Kamiński A.: Convolution, product and Fourier transform of distributions.Studia Math. 74 (1982), 83-96. MR 0675434 |
| Reference:
|
[7] Langebruch M.: Randverteilungen von Nullösungen hypoelliptischer Differentialgleichungen.Manuscripta Math. 26 (1978), 17-35. MR 0513144 |
| Reference:
|
[8] Li Banghe: Nonstandard analysis and multiplication of distributions.Scientia Scinica, Ser. A 21 (1978), 561-585. MR 0513744 |
| Reference:
|
[9] Li Banghe, Li Yaqing: Nonstandard analysis and multiplication of distributions in any dimension.Scientia Scinica, Ser. A 28 (1985), 716-726. Zbl 0597.46034, MR 0813857 |
| Reference:
|
[10] Li Banghe, Li Yaqing: On the harmonic and analytic representations of distributions.Scientia Scinica, Ser. A 28 (1985), 923-937. Zbl 0597.46039 |
| Reference:
|
[11] Liu Shangping: Distributions in $\Cal D'(\Bbb R^n)$ as boundary values of harmonic functions.Scientia Scinica, Ser. A 27 (1984), 897-904. MR 0767622 |
| Reference:
|
[12] Oberguggenberger M.: Products of distributions: Nonstandard methods.Zeitschr. Anal. Anw. 7 (1988), 347-365; Correction: {Zeitschr. Anal. Anw.} 10 (1991), 263-264. Zbl 0662.46048, MR 0963445 |
| Reference:
|
[13] Oberguggenberger M.: Multiplication of distributions and applications to partial differential equations.Pitman Research Notes in Mathematics, vol. 259, 1992. Zbl 0818.46036, MR 1187755 |
| Reference:
|
[14] Schwartz L.: Sur l'impossibilité de la multiplication des distributions.C.R. Acad. Sci., Paris 239 (1954), 847-848. Zbl 0056.10602, MR 0064324 |
| Reference:
|
[15] Schwartz L.: Théorie des distributions.Hermann, Paris, nouv. edition, 1966. Zbl 0962.46025, MR 0209834 |
| Reference:
|
[16] Tillmann H.G.: Darstellung der Schwartzschen Distributionen durch analytische Funktionen.Math. Zeitschr. 77 (1961), 106-124. Zbl 0099.09703, MR 0139002 |
| Reference:
|
[17] Wawak R.: On the Colombeau product of distributions.in Generalized functions and convergence, P. Antosik and A. Kamiński, eds., World Scientific, Singapore, 1990, pp.279-284. MR 1085515 |
| . |
