Schwartz Functions on Real Algebraic Varieties

被引：4

作者：

Elazar, Boaz ^{[1
]}

Shaviv, Ary ^{[1
]}

机构：

[1] Weizmann Inst Sci, Fac Math & Comp Sci, IL-76100 Rehovot, Israel

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2018年 / 70卷 / 05期

关键词：

real algebraic geometry; Schwartz function; tempered distribution; WHITNEYS EXTENSION PROBLEM; SUBANALYTIC SETS;

D O I：

10.4153/CJM-2017-042-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define Schwartz functions, tempered functions, and tempered distributions on (possibly singular) real algebraic varieties. We prove that all classical properties of these spaces, defined previously on affine spaces and on Nash manifolds, also hold in the case of affine real algebraic varieties, and give partial results for the non-affine case.

引用

页码：1008 / 1037

页数：30

共 50 条

[31] Real torus actions on real affine algebraic varieties
Gillard, Pierre-Alexandre
MATHEMATISCHE ZEITSCHRIFT, 2022, 301 (02) : 1507 - 1536
[32] Divisors on real algebraic varieties without real points
Joost van Hamel
manuscripta mathematica, 1999, 98 : 409 - 424
[33] Algebraic and real K-theory of Real varieties
Karoubi, M
Weibel, C
TOPOLOGY, 2003, 42 (04) : 715 - 742
[34] Real torus actions on real affine algebraic varieties
Pierre-Alexandre Gillard
Mathematische Zeitschrift, 2022, 301 : 1507 - 1536
[35] Divisors on real algebraic varieties without real points
van Hamel, J
MANUSCRIPTA MATHEMATICA, 1999, 98 (04) : 409 - 424
[36] Real algebraic functions, real algebraic curves and their moduli spaces
Frediani, P
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 1999, 2A : 33 - 36
[37] SPACES OF ALGEBRAIC AND CONTINUOUS MAPS BETWEEN REAL ALGEBRAIC VARIETIES
Adamaszek, Michal
Kozlowski, Andrzej
Yamaguchi, Kohhei
QUARTERLY JOURNAL OF MATHEMATICS, 2011, 62 (04): : 771 - 790
[38] Quotients of real algebraic G varieties and algebraic realization problems
Suh, DY
OSAKA JOURNAL OF MATHEMATICS, 1996, 33 (02) : 399 - 410
[39] Growth of transcendental entire functions on algebraic varieties
Einstein-Matthews, SM
Lutterodt, CH
ISRAEL JOURNAL OF MATHEMATICS, 1999, 109 (1) : 253 - 271
[40] Growth of transcendental entire functions on algebraic varieties
Stanley M. Einstein-Matthews
Clement H. Lutterodt
Israel Journal of Mathematics, 1999, 109 : 253 - 271

← 1 2 3 4 5 →