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91: １３２人目の素数さん [] 2023/03/07(火) 18:35:39.96 ID:6myOW2uQ

>>75 素人なので、知らない人で調べたことを貼りますね

https://en.wikipedia.org/wiki/Abhyankar
Abhyankar is a surname native to the Indian state of Maharashtra. Abhyankar surname is found among Chitpavan Brahmin community.[1][2]
Notable people
https://en.wikipedia.org/wiki/Shreeram_Shankar_Abhyankar
Shreeram Shankar Abhyankar
Shreeram Shankar Abhyankar (22 July 1930 ? 2 November 2012)[1][2] was an Indian American mathematician known for his contributions to algebraic geometry.

https://upload.wikimedia.org/wikipedia/commons/e/ee/Abhyankar_Grothendieck.jpg
Shreeram Abhyankar (right) with Alexander Grothendieck (left), Michael Artin in the background, at Montreal, Quebec, Canada in 1970.

Career
Abhyankar was appointed the Marshall Distinguished Professor of Mathematics at Purdue in 1967. His research topics include algebraic geometry (particularly resolution of singularities, a field in which he made significant progress over fields of finite characteristic), commutative algebra, local algebra, valuation theory, theory of functions of several complex variables, quantum electrodynamics, circuit theory, invariant theory, combinatorics, computer-aided design, and robotics. He popularized the Jacobian conjecture.

http://rio2016.5ch.net/test/read.cgi/math/1677671318/91

543: １３２人目の素数さん [] 2023/03/18(土) 23:18:41.86 ID:M09HE8oG

>>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.

つづく

http://rio2016.5ch.net/test/read.cgi/math/1677671318/543

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