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Schwartz Functions on Real Algebraic Varieties

Published online by Cambridge University Press:  20 November 2018

Boaz Elazar  and
Ary Shaviv
Boaz Elazar
Affiliation:
Faculty of Mathematics and Computer Science, Weizmann Institute of Science, Rehovot 76100, Israel, e-mail: boaz.elazar@weizmann.ac.il , ary.shaviv@weizmann.ac.il
Ary Shaviv
Affiliation:
Faculty of Mathematics and Computer Science, Weizmann Institute of Science, Rehovot 76100, Israel, e-mail: boaz.elazar@weizmann.ac.il , ary.shaviv@weizmann.ac.il
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Abstract

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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

14P9914P0522E4546A1146F05real algebraic geometrySchwartz functiontempered distribution
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 70 , Issue 5 , 01 October 2018 , pp. 1008 - 1037
Copyright
Copyright © Canadian Mathematical Society 2018

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