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543(2): １３２人目の素数さん [] 2023/03/18(土)23:18 ID:M09HE8oG(20/24)
>>535
>https://en.wikipedia.org/wiki/Reproducing_kernel_Hilbert_space
>Reproducing kernel Hilbert space

追加引用 （一部google訳）
https://upload.wikimedia.org/wikipedia/commons/6/65/Different_Views_on_RKHS.png

図は、RKHS を表示するための関連するさまざまなアプローチを示しています。

RKHS ではない関数のヒルベルト空間を構成することは、完全に単純ではありません。[1]ただし、いくつかの例が見つかっています。[2] [3]

It is not entirely straightforward to construct a Hilbert space of functions which is not an RKHS.[1] Some examples, however, have been found.[2][3]

L2 spaces are not Hilbert spaces of functions (and hence not RKHSs), but rather Hilbert spaces of equivalence classes of functions (for example, the functions
f and g defined by f(x)=0 and
g(x)=1_Q are equivalent in L2). However, there are RKHSs in which the norm is an L2-norm, such as the space of band-limited functions (see the example below).

An RKHS is associated with a kernel that reproduces every function in the space in the sense that for every x in the set on which the functions are defined, "evaluation at x" can be performed by taking an inner product with a function determined by the kernel. Such a reproducing kernel exists if and only if every evaluation functional is continuous.

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