Matemati\u011fin bir dal\u0131 olan karma\u015f\u0131k analizde Mergelyan teoremi, Ermeni matematik\u00e7i Sergei Nikitovi\u00e7 Mergelyan taraf\u0131ndan 1951’de kan\u0131tlanm\u0131\u015f ve Mergelyan’a ithafen isimlendirilmi\u015f bir matematiksel sonu\u00e7tur. Mergelyan teoremi \u015funu ifade etmektedir:
\nK karma\u015f\u0131k d\u00fczlem C ‘nin t\u0131k\u0131z bir altk\u00fcmesi olsun \u00f6yle ki C \\ K ‘de ba\u011flant\u0131l\u0131 olsun. Bu halde, bir f: K->C fonksiyonu K \u00fczerinde s\u00fcrekliyse ve f ‘nin K ‘nin i\u00e7 b\u00f6lgesindeki s\u0131n\u0131rlamas\u0131 olan f|int(K) holomorfikse; f, K \u00fczerinde polinomlarla d\u00fczg\u00fcn yak\u0131nsanabilir. (Burada int(K) ifadesi K k\u00fcmesinin i\u00e7ini (i\u00e7 b\u00f6lge) temsil etmektedir.)
\nMergelyan teoremi, Stone-Weierstrass teoreminin ve Runge teoreminin en son geli\u015fmi\u015f ve genelle\u015ftirilmi\u015f halidir. Bir klasik olan polinomlarla yakla\u015fma problemine tam bir \u00e7\u00f6z\u00fcm vermektedir.
\nC \\ K ba\u011flant\u0131l\u0131 olmad\u0131\u011f\u0131 zaman, ba\u015flang\u0131\u00e7taki yakla\u015f\u0131m problemindeki polinomlar yerini rasyonel fonksiyonlara b\u0131rak\u0131rlar. Bu daha ileriki rasyonel yakla\u015f\u0131m probleminin \u00e7\u00f6z\u00fcm\u00fcn\u00fcn \u00f6nemli bir ad\u0131m\u0131 da ayr\u0131ca S. N. Mergelyan taraf\u0131ndan 1952’de ileri s\u00fcr\u00fclm\u00fc\u015ft\u00fcr. Rasyonel yakla\u015f\u0131mdaki daha derin sonu\u00e7lar \u00f6zellikle A. G. Vitu\u015fkin’e aittir.
\nMergelyan teoreminin tarihi 1951 iken, Weierstrass ve Runge teoremleri 1885’te ileri s\u00fcr\u00fclm\u00fc\u015ft\u00fcr. Aradaki bu uzun zaman fark\u0131 asl\u0131nda \u00e7ok da s\u00fcrpriz de\u011fildir \u00e7\u00fcnk\u00fc Mergelyan teoremi Mergelyan taraf\u0131ndan yarat\u0131lm\u0131\u015f yeni g\u00fc\u00e7l\u00fc metodlar\u0131 kullanmaktad\u0131r. Weierstrass ve Runge’den sonra \u00f6zellikle Walsh, Keldysh, Lavrentiev gibi matematik\u00e7ileri de i\u00e7eren bir\u00e7ok matematik\u00e7i de ayn\u0131 problem \u00fczerinde \u00e7al\u0131\u015f\u0131yordu. Mergelyan taraf\u0131ndan ileri s\u00fcr\u00fclen kan\u0131t\u0131n metodu yap\u0131sald\u0131r ve sonucun bilinen tek yap\u0131sal kan\u0131t\u0131d\u0131r.<\/p>\n","protected":false},"excerpt":{"rendered":"
Matemati\u011fin bir dal\u0131 olan karma\u015f\u0131k analizde Mergelyan teoremi, Ermeni matematik\u00e7i Sergei Nikitovi\u00e7 Mergelyan taraf\u0131ndan 1951’de kan\u0131tlanm\u0131\u015f ve Mergelyan’a ithafen isimlendirilmi\u015f bir matematiksel sonu\u00e7tur. Mergelyan teoremi \u015funu ifade etmektedir: K karma\u015f\u0131k d\u00fczlem C ‘nin t\u0131k\u0131z bir altk\u00fcmesi olsun \u00f6yle ki C \\ K ‘de ba\u011flant\u0131l\u0131 olsun. Bu halde, bir f: K->C fonksiyonu K \u00fczerinde s\u00fcrekliyse ve …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1404,1403],"tags":[7493,7399],"class_list":["post-3246","post","type-post","status-publish","format-standard","hentry","category-matematik-odevleri","category-odevler","tag-mergelyan-teoremi","tag-polinomlar"],"_links":{"self":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3246","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/comments?post=3246"}],"version-history":[{"count":0,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3246\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/media?parent=3246"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/categories?post=3246"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/tags?post=3246"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}