Constructive nonstandard representations of generalized functions

被引：6

作者：

Palmgren, E ^{[1
]}

机构：

[1] Uppsala Univ, Dept Math, S-75106 Uppsala, Sweden

来源：

INDAGATIONES MATHEMATICAE-NEW SERIES | 2000年 / 11卷 / 01期

关键词：

D O I：

10.1016/S0019-3577(00)88579-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using techniques of nonstandard analysis Abraham Robinson showed that it is possible to represent each Schwartz distribution T as an integral T(phi) = integral f phi, where f is some nonstandard smooth function. We show that the theory based on this representation can be developed within a constructive setting.

引用

页码：129 / 138

页数：10

共 50 条

[31] Nonstandard representations of the canonical commutation relations
Yamashita, H
Ozawa, M
REVIEWS IN MATHEMATICAL PHYSICS, 2000, 12 (11) : 1407 - 1427
[32] Representations of the small nonstandard quantum groups
Su, Dong
Yang, Shilin
COMMUNICATIONS IN ALGEBRA, 2019, 47 (12) : 5039 - 5062
[33] Nonstandard representations of locally compact groups
Lyubetskii, V. A.
Pirogov, S. A.
MATHEMATICAL NOTES, 2007, 82 (3-4) : 341 - 346
[34] Nonstandard representations of locally compact groups
V. A. Lyubetskii
S. A. Pirogov
Mathematical Notes, 2007, 82 : 341 - 346
[35] NONSTANDARD REPRESENTATIONS OF DISTRIBUTIONS .2.
KINOSHITA, M
OSAKA JOURNAL OF MATHEMATICS, 1990, 27 (04) : 843 - 861
[36] Representations of nonstandard Poincare Hopf algebras
Yang, Shilin
Yang, Yichuan
COMMUNICATIONS IN ALGEBRA, 2008, 36 (02) : 732 - 748
[37] A nonstandard proof of a lemma from constructive measure theory
Ross, David A.
MATHEMATICAL LOGIC QUARTERLY, 2006, 52 (05) : 494 - 497
[38] The constructive content of nonstandard measure existence proofs - Is there any?
Ross, DA
REUNITING THE ANTIPODES - CONSTRUCTIVE AND NONSTANDARD VIEWS OF THE CONTINUUM, 2001, 306 : 229 - 239
[39] Reuniting the antipodes - constructive and nonstandard views of the continuum.
Fletcher, P
HISTORY AND PHILOSOPHY OF LOGIC, 2002, 23 (04) : 301 - 303
[40] Nonstandard representations of processes in dynamical systems
Mijajlovic, Zarko
Pejovic, Nadezda
Ninkovic, Slobodan
FLOWS, BOUNDARIES, INTERACTIONS, 2007, 934 : 151 - +

← 1 2 3 4 5 →