CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

Author's Draft

Schwartz functions on real algebraic varieties

  • Boaz Elazar,
    Department of Mathematics and Computer Science, Weizmann Institute of Science, Rehovot 76100, Israel
  • Ary Shaviv,
    Department of Mathematics and Computer Science, Weizmann Institute of Science, Rehovot 76100, Israel
Format:   LaTeX   MathJax   PDF  

Abstract

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.
Keywords: real algebraic geometry, Schwartz function, tempered distribution real algebraic geometry, Schwartz function, tempered distribution
MSC Classifications: 14P99, 14P05, 22E45, 46A11, 46F05 show english descriptions None of the above, but in this section
Real algebraic sets [See also 12Dxx, 13P30]
Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05}
Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
Topological linear spaces of test functions, distributions and ultradistributions [See also 46E10, 46E35]
14P99 - None of the above, but in this section
14P05 - Real algebraic sets [See also 12Dxx, 13P30]
22E45 - Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05}
46A11 - Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
46F05 - Topological linear spaces of test functions, distributions and ultradistributions [See also 46E10, 46E35]
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/