کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4665704 | 1633826 | 2014 | 56 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Approximation on Nash sets with monomial singularities
ترجمه فارسی عنوان
تقریبی در مجموعه نوش با تکینگی های تک هسته ای
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
چکیده انگلیسی
This paper is devoted to the approximation of differentiable semialgebraic functions by Nash functions. Approximation by Nash functions is known for semialgebraic functions defined on an affine Nash manifold M, and here we extend it to functions defined on Nash sets XâM whose singularities are monomial. To that end we discuss first finiteness and weak normality for such sets X. Namely, we prove that (i) X is the union of finitely many open subsets, each Nash diffeomorphic to a finite union of coordinate linear varieties of an affine space, and (ii) every function on X which is Nash on every irreducible component of X extends to a Nash function on M. Then we can obtain approximation for semialgebraic functions and even for certain semialgebraic maps on Nash sets with monomial singularities. As a nice consequence we show that m-dimensional affine Nash manifolds with divisorial corners which are class k semialgebraically diffeomorphic, for k>m2, are also Nash diffeomorphic.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 262, 10 September 2014, Pages 59-114
Journal: Advances in Mathematics - Volume 262, 10 September 2014, Pages 59-114
نویسندگان
ElÃas Baro, José F. Fernando, Jesús M. Ruiz,