@techreport{oai:ipsj.ixsq.nii.ac.jp:00232503,
 author = {Akira, Tanaka and Akira, Tanaka},
 issue = {33},
 month = {Feb},
 note = {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.},
 title = {Kernel-Induced Sampling Theorem for A Class of Mapping-Prescribed Reproducing Kernel Hilbert Spaces},
 year = {2024}
}