. "1950"^^ . . . "Reproducing kernel Hilbert space"@en . "3"^^ . . . "In functional analysis (a branch of mathematics), a reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which pointwise evaluation is a continuous linear functional. Equivalently, they are spaces that can be defined by reproducing kernels. The subject was originally and simultaneously developed by Nachman Aronszajn (1907\u20131980) and Stefan Bergman (1895\u20131977) in 1950.In this article we assume that Hilbert spaces are complex."@en . . . . "Noyau reproduisant"@fr . "In functional analysis (a branch of mathematics), a reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which pointwise evaluation is a continuous linear functional. Equivalently, they are spaces that can be defined by reproducing kernels. The subject was originally and simultaneously developed by Nachman Aronszajn (1907\u20131980) and Stefan Bergman (1895\u20131977) in 1950.In this article we assume that Hilbert spaces are complex. The main reason for this is that many of the examples of reproducing kernel Hilbert spaces are spaces of analytic functions, although some real Hilbert spaces also have reproducing kernels. A key motivation for reproducing kernel hilbert spaces in machine learning is the Representer theorem which says that any function in an RKHS that classifies a set of sample points can be defined as a linear combination of the canonical feature maps of those points.An important subset of the reproducing kernel Hilbert spaces are the reproducing kernel Hilbert spaces associated to a continuous kernel. These spaces have wide applications, including complex analysis, harmonic analysis, quantum mechanics, statistics and machine learning."@en . . . . . . . . "68"^^ . "Do\u011Furan \u00E7ekirdekli Hilbert uzay\u0131"@tr . . . . . "Matemati\u011Fin bir alt dal\u0131 olan fonksiyonel analizde, do\u011Furan \u00E7ekirdekli Hilbert uzay\u0131 noktasal de\u011Ferlemenin bir s\u00FCrekli do\u011Frusal fonksiyonel oldu\u011Fu bir fonksiyonlar Hilbert uzay\u0131d\u0131r. Burada, fonksiyonlar Hilbert uzay\u0131ndan kas\u0131t, bahsi ge\u00E7en uzay\u0131n \u00F6\u011Felerinin fonksiyonlar oldu\u011Fudur. Yani s\u00F6z konusu uzay bir fonksiyon uzay\u0131d\u0131r; bununla birlikte ayn\u0131 zamanda Hilbert uzay\u0131 \u00F6zelli\u011Fi de ta\u015F\u0131maktad\u0131r. Benzer bir \u015Fekilde, bu t\u00FCr uzaylar do\u011Furan \u00E7ekirdekler taraf\u0131ndan da tan\u0131mlanabilirler. Bu terimi ilk defa ve ayn\u0131 zamanda Nachman Aronszajn (1907\u20131980) ve Stefan Bergman (1895\u20131977) adl\u0131 matematik\u00E7iler 1950'de ortaya at\u0131p geli\u015Ftirmi\u015Flerdir.Her ne kadar baz\u0131 ger\u00E7el Hilbert uzaylar\u0131n\u0131n do\u011Furan \u00E7ekirdekli olma \u00F6zelli\u011Fi olsa da, bu t\u00FCr uzaylara verilebilecek \u00F6rneklerin bir\u00E7o\u011Fu analitik fonksiyon uzaylar\u0131ndan gelmektedir. Bu sebeple, analitik fonksiyonlar\u0131n karma\u015F\u0131k de\u011Ferli fonksiyonlar oldu\u011Funu da g\u00F6z\u00F6n\u00FCne alarak, Hilbert uzaylar\u0131n\u0131n de\u011Fi\u015Fkenlerinin karma\u015F\u0131k say\u0131 oldu\u011Funu kabul edelim.Do\u011Furan \u00E7ekirdekli Hilbert uzaylar\u0131n\u0131n \u00F6nemli bir altk\u00FCmesi yine bu t\u00FCr uzaylar\u0131n s\u00FCrekli bir \u00E7ekirdekle ilintili olanlar\u0131d\u0131r. Bu uzaylar\u0131n karma\u015F\u0131k analiz, kuantum mekani\u011Fi ve harmonik analizi de i\u00E7erecek \u015Fekilde geni\u015F bir uygulamas\u0131 mevcuttur."@tr . "337"^^ . . "11358"^^ . "Theory of Reproducing Kernels"@fr . "5824676"^^ . . . . . . "Trans. Amer. Math. Soc."@fr . "Nachman"@fr . . . . . "31"^^ . . . . . . . . . . "Aronszajn"@fr . . "Matemati\u011Fin bir alt dal\u0131 olan fonksiyonel analizde, do\u011Furan \u00E7ekirdekli Hilbert uzay\u0131 noktasal de\u011Ferlemenin bir s\u00FCrekli do\u011Frusal fonksiyonel oldu\u011Fu bir fonksiyonlar Hilbert uzay\u0131d\u0131r. Burada, fonksiyonlar Hilbert uzay\u0131ndan kas\u0131t, bahsi ge\u00E7en uzay\u0131n \u00F6\u011Felerinin fonksiyonlar oldu\u011Fudur. Yani s\u00F6z konusu uzay bir fonksiyon uzay\u0131d\u0131r; bununla birlikte ayn\u0131 zamanda Hilbert uzay\u0131 \u00F6zelli\u011Fi de ta\u015F\u0131maktad\u0131r. Benzer bir \u015Fekilde, bu t\u00FCr uzaylar do\u011Furan \u00E7ekirdekler taraf\u0131ndan da tan\u0131mlanabilirler."@tr . "95105810"^^ . . "en"@fr . . . . . "Transactions of the American Mathematical Society"@fr . . .