کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4615178 | 1339309 | 2015 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Explicit representations of spaces of smooth functions and distributions
ترجمه فارسی عنوان
تظاهرات صریح فضاهای توابع و توابع صاف
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
چکیده انگلیسی
We provide an explicit isomorphism between the space of smooth functions E(Rd) and its sequence space representation sâËCN which isomorphically maps various spaces of smooth functions onto their sequence-space representation, including the space D(Rd), of test functions, the space of Schwartz functions S(Rd) and the space of “p-integrable smooth functions” DLp(Rd). By restriction and transposition, this isomorphism yields an isomorphism between the space of distributions Dâ²(Rd) and its sequence space representation sâ²âËÏCN which analogously maps various spaces of distributions isomorphically onto their sequence space representation. We use this isomorphism to construct both a common Schauder basis for these spaces of smooth functions and a common Schauder basis for the corresponding spaces of distributions.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 424, Issue 2, 15 April 2015, Pages 1491-1505
Journal: Journal of Mathematical Analysis and Applications - Volume 424, Issue 2, 15 April 2015, Pages 1491-1505
نویسندگان
Christian Bargetz,