About: Bergman kernel

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Bergman kernel Goto Sponge NotDistinct Permalink

An Entity of Type : owl:Thing, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)
QRcode icon

http://dbpedia.demo.openlinksw.com/c/d8TQD5t9h

In functional analysis (a branch of mathematics), a reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation is a continuous linear functional. Roughly speaking, this means that if two functions and in the RKHS are close in norm, i.e., is small, then and are also pointwise close, i.e., is small for all . The converse does not need to be true. It is not entirely straightforward to construct a Hilbert space of functions which is not an RKHS. Some examples, however, have been found.

Attributes	Values
rdfs:label	Espace de Hilbert à noyau reproduisant (fr) 재생핵 힐베르트 공간 (ko) Reproducing kernel Hilbert space (en) Przestrzeń Hilberta z jądrem reprodukującym (pl)
rdfs:comment	함수해석학에서, 재생핵 힐베르트 공간(再生核Hilbert空間, 영어: reproducing kernel Hilbert space)은 값매김 연산자가 유계 작용소인, 함수로 구성된 힐베르트 공간이다. 함수의 동치류로 구성된 르베그 공간 따위와 달리, 재생핵 힐베르트 공간은 함수로 구성되어야 한다. (르베그 공간의 경우, 주어진 점에서 함수 동치류의 원소들이 임의의 값을 가질 수 있어 값매김 연산자를 정의할 수 없다.) (ko) In functional analysis (a branch of mathematics), a reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation is a continuous linear functional. Roughly speaking, this means that if two functions and in the RKHS are close in norm, i.e., is small, then and are also pointwise close, i.e., is small for all . The converse does not need to be true. It is not entirely straightforward to construct a Hilbert space of functions which is not an RKHS. Some examples, however, have been found. (en) En analyse fonctionnelle, un espace de Hilbert à noyau reproduisant est un espace de Hilbert de fonctions pour lequel toutes les applications sont des formes linéaires continues. De manière équivalente, il existe des espaces qu'on peut définir par des noyaux reproduisants. Le sujet a été originellement et simultanément développé par Nachman Aronszajn et Stefan Bergman en 1950. Les espaces de Hilbert à noyau reproduisant sont parfois désignés sous l’acronyme issu du titre anglais RKHS, pour Reproducing Kernel Hilbert Space. (fr) W analizie funkcjonalnej (gałąź matematyki) przestrzeń Hilberta z jądrem reprodukującym (ang. Reproducing Kernel Hilbert Space, RKHS) jest przestrzenią Hilberta z iloczynem skalarnym funkcji określonych na zbiorze U o wartościach w ciele liczb rzeczywistych lub zespolonych, w której wszystkie funkcjonały ewaluacji, tzn. funkcjonały są ciągłe, tzn. dla każdego istnieje taka stała , że , gdzie stała nie zależy of wyboru funkcji . Jeśli funkcjonały ewaluacji są ciągłe, to na mocy Twierdzenia Riesza dla każdego istnieje takie , że dla każdej funkcji . Funkcję określoną w następujący sposób: (pl)
foaf:depiction
dct:subject	Hilbert space
Wikipage page ID	651196 (xsd:integer)
Wikipage revision ID	1109916316 (xsd:integer)
Link from a Wikipage to another Wikipage	Quantum mechanics Mercer's theorem Real-valued function Bergman kernel Bergman space Holomorphic function Hilbert space Riesz representation theorem Cutoff frequency Integral equation Completion (metric space) Complex analysis Continuous function Mathematics Salomon Bochner Functional (mathematics) Grace Wahba Boundary value problem Bounded operator Multi-task learning Nachman Aronszajn Representer theorem Stanisław Zaremba (mathematician) Stefan Bergman Empirical risk minimization Functional analysis Harmonic analysis Kernel embedding of distributions Bandlimiting Cauchy–Schwarz inequality H square James Mercer (mathematician) Linear combination E. H. Moore Fourier transform Fourier inversion theorem Rectifier (neural networks) Gábor Szegő Harmonic function Hilbert space Isomorphic Karhunen–Loève theorem Biharmonic equation Dirac delta function Borel measure Bulletin of the AMS Positive-definite kernel Positive definite Spectral theorem Continuous function (topology) Inner product Cartesian closed category Radial basis function kernel Set (mathematics) Similarity measure Kernel trick Computational learning theory Square-integrable function Manifold regularization Transactions of the American Mathematical Society Positive definite kernel Analytic functions Kernel PCA Plancherel's theorem Unit disc
Link from a Wikipage to an external page	https://www.mit.edu/~9.520/scribe-notes/class03_gdurett.pdf, http://www.jmlr.org/papers/volume13/zhang12a/zhang12a.pdf http://www.stat.wisc.edu/~wahba/ftp1/oldie/kw71.pdf http://www.thesis.bilkent.edu.tr/0002953.pdf, http://www.math.uh.edu/~vern/rkhs.pdf. https://arxiv.org/abs/1106.6251, http://www.siam.org/books/
sameAs	Bergman kernel Bergman kernel Bergman kernel Bergman kernel Bergman kernel Bergman kernel Bergman kernel
dbp:wikiPageUsesTemplate	dbt:Citation_needed dbt:Cite_journal dbt:Clarify dbt:NumBlk dbt:Reflist dbt:EquationRef dbt:EquationNote dbt:ArXiv

Faceted Search & Find service v1.17_git147 as of Sep 06 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3331 as of Sep 2 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 52 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software