Seminar in Real and Complex Geometry

Thursday, November 2, 2017, 11:00-12:00, Schreiber building, room 209

Boaz Elazar, Weizmann Institute

Schwartz Functions On Algebraic And QN Varieties


We define Schwartz functions and tempered functions on affine real algebraic varieties, which might be singular. We prove that some of the important classical properties of these functions, such as partition of unity, characterization on open subsets, etc., continue to hold in this case. The study of this category (joint with Ary Shaviv) was later enlarged to include Nash manifolds. The new category was named Quasi Nash and indeed it contains the Nash category as full subcategory, and the algebraic case as (non full) subcategory. Furthermore, the new category enables us to prove some non-affine properties which we were unable to show in the general algebraic case.