2026-03-09T19:04:19Z https://ipsj.ixsq.nii.ac.jp/oai

oai:ipsj.ixsq.nii.ac.jp:00232503 2025-01-19T10:25:35Z 1164:5159:11541:11549

Kernel-Induced Sampling Theorem for A Class of Mapping-Prescribed Reproducing Kernel Hilbert Spaces Kernel-Induced Sampling Theorem for A Class of Mapping-Prescribed Reproducing Kernel Hilbert Spaces Akira, Tanaka Akira, Tanaka SIP1 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. 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. technical report 情報処理学会 2024-02-22 application/pdf 研究報告音声言語情報処理（SLP） 33 2024-SLP-151 1 6 2188-8663 AN10442647 https://ipsj.ixsq.nii.ac.jp/record/232503/files/IPSJ-SLP24151033.pdf eng