WEKO3
アイテム
On Convergence of Fourier Inverse Transforms for Piecewise Smooth Radial Functions in R^n
https://doi.org/10.15066/00000224
https://doi.org/10.15066/00000224a3764665-b79d-4c39-9964-db3ed17ec520
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
110006556359 (524.1 kB)
|
|
| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2014-10-16 | |||||
| タイトル | ||||||
| タイトル | On Convergence of Fourier Inverse Transforms for Piecewise Smooth Radial Functions in R^n | |||||
| タイトル | ||||||
| タイトル | On Convergence of Fourier Inverse Transforms for Piecewise Smooth Radial Functions in R^n | |||||
| 言語 | en | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
| 資源タイプ | departmental bulletin paper | |||||
| ID登録 | ||||||
| ID登録 | 10.15066/00000224 | |||||
| ID登録タイプ | JaLC | |||||
| 著者 |
Kojima, Michitaka
× Kojima, Michitaka |
|||||
| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | For a function f∈L^p(R^n)(1≦p≦2), we denote by (S_Rf)(x)(R>0) the spherical partial sums of Fourier inverse transform of f defined by [numerical formula]and let =f(x)=F(|x|) be radial with support in {|x|≦α} (α>0). In this note, in particular, when n≧3, we give a detailed proof of the fact that, for smooth F∈C^<l+2>([0,α]), l=[(n-3)/2], vanishing in a neighborhood of the origin, a necessary and sufficient condition under which we have lim_<R→∞>(S_Rf)(0)=0 is the validity of F^(k)(α)=0 for all k=0, 1,...,l. This fact gives a negative answer to the localization problem concerning of (S_Rf)(x) for piecewise smooth radial function f. | |||||
| 内容記述 | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | For a function f∈L^p(R^n)(1≦p≦2), we denote by (S_Rf)(x)(R>0) the spherical partial sums of Fourier inverse transform of f defined by [numerical formula]and let =f(x)=F(|x|) be radial with support in {|x|≦α} (α>0). In this note, in particular, when n≧3, we give a detailed proof of the fact that, for smooth F∈C^<l+2>([0,α]), l=[(n-3)/2], vanishing in a neighborhood of the origin, a necessary and sufficient condition under which we have lim_<R→∞>(S_Rf)(0)=0 is the validity of F^(k)(α)=0 for all k=0, 1,...,l. This fact gives a negative answer to the localization problem concerning of (S_Rf)(x) for piecewise smooth radial function f. | |||||
| 書誌情報 |
北陸大学紀要 en : Bulletin of Hokuriku University 巻 19, p. 13-30, 発行日 1995-12-31 |
|||||
| 出版者 | ||||||
| 出版者 | 北陸大学 | |||||
| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 0387074X | |||||
| 書誌レコードID | ||||||
| 収録物識別子タイプ | NCID | |||||
| 収録物識別子 | AN00227706 | |||||
| 論文ID（NAID） | ||||||
| 識別子タイプ | NAID | |||||
| 関連識別子 | 110006556359 | |||||
