کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4616068 | 1339338 | 2014 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the spaces OCm of John Horváth
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
In the table (on p. 442) of John Horváth's textbook “Topological Vector Spaces and Distributions”, the questions for an explicit description of the topology of OCm by seminorms, for the completeness and for the metrizability of the space OCm remained open, whereas, for m=â, the completeness was shown by A. Grothendieck in his thesis. We resolve these questions in Proposition 1, Proposition 2, Proposition 3. In Proposition 4, Proposition 5, Proposition 6, Proposition 7, we investigate multiplication and convolution in the spaces Sm, OCm, Sâ²m, OCâ²m analogously to the treatment in the spaces Em, Dm, Dâ²m, Eâ²m in J. Horváth's book (Ch. 4, §6 Multiplication, §9 Convolution, §10 Regularization). In Section 6, the multiplication and convolution of holomorphic functions with values in Sm, OCm, Sâ²m, OCâ²m are investigated analogously to J. Horváth's treatment of holomorphic functions with values in the spaces Em, Dm, Dâ²m, Eâ²m.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 415, Issue 1, 1 July 2014, Pages 62-74
Journal: Journal of Mathematical Analysis and Applications - Volume 415, Issue 1, 1 July 2014, Pages 62-74
نویسندگان
Norbert Ortner, Peter Wagner,