Kernel-Induced Sampling Theorem for A Class of Mapping-Prescribed Reproducing Kernel Hilbert Spaces

• Item type: SIG Technical Reports(1)
• 公開日: 2024-02-22
• タイトル: Kernel-Induced Sampling Theorem for A Class of Mapping-Prescribed Reproducing Kernel Hilbert Spaces
• タイトル / 言語: en
• タイトル: Kernel-Induced Sampling Theorem for A Class of Mapping-Prescribed Reproducing Kernel Hilbert Spaces
• 言語: eng
• キーワード / 主題Scheme: Other
• キーワード / 主題: SIP1
• 資源タイプ / 資源タイプ識別子: http://purl.org/coar/resource_type/c_18gh
• 資源タイプ: technical report
• 著者所属: Faculty of Information Science and Technology, Hokkaido University
• 著者所属(英): en
• 著者所属(英): Faculty of Information Science and Technology, Hokkaido University
• 著者名: Akira, Tanaka
• 著者名(英): Akira, Tanaka
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: A reproducing kernel is often interpreted as an inner product of two input vectors mapped into a certain space. On the contrary, if a mapping and a metric of the range space of the mapping are specified, the corresponding reproducing kernel and the unique corresponding reproducing kernel Hilbert space are automatically specified. In this paper, we introduce a class of reproducing kernel Hilbert spaces prescribed by an arbitrarily fixed mapping, and discuss properties of the spaces. Moreover, we give a necessary and sufficient condition that leads the sampling theorem (perfect reconstruction of a function from sampling points) for a reproducing kernel Hilbert space in the class. In addition, we theoretically analyze the role of a metric, by which one reproducing kernel Hilbert space among the class is specified, of the class in the function reconstruction process.
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: A reproducing kernel is often interpreted as an inner product of two input vectors mapped into a certain space. On the contrary, if a mapping and a metric of the range space of the mapping are specified, the corresponding reproducing kernel and the unique corresponding reproducing kernel Hilbert space are automatically specified. In this paper, we introduce a class of reproducing kernel Hilbert spaces prescribed by an arbitrarily fixed mapping, and discuss properties of the spaces. Moreover, we give a necessary and sufficient condition that leads the sampling theorem (perfect reconstruction of a function from sampling points) for a reproducing kernel Hilbert space in the class. In addition, we theoretically analyze the role of a metric, by which one reproducing kernel Hilbert space among the class is specified, of the class in the function reconstruction process.
• 書誌レコードID / 収録物識別子タイプ: NCID
• 書誌レコードID / 収録物識別子: AN10442647
• 書誌情報: 研究報告音声言語情報処理（SLP）; 巻 2024-SLP-151, 号 33, p. 1-6, 発行日 2024-02-22
• ISSN / 収録物識別子タイプ: ISSN
• ISSN / 収録物識別子: 2188-8663
• Notice: SIG Technical Reports are nonrefereed and hence may later appear in any journals, conferences, symposia, etc.
• 出版者 / 言語: ja
• 出版者: 情報処理学会