{"product_id":"approximation-of-harmonic-functions-by-universal-overconvergent-series-von-innocent-tamptse","title":"Approximation of harmonic functions by universal overconvergent series","description":"\u003cp\u003eWe study the approximation of harmonic functions by  universal overconvergent series. Most of the results established are analogues of those obtained in the  case of approximation of holomorphic functions by  such series. In the case of holomorphic functions,  the approximation is made for functions which are  continuous on a compact set and holomorphic inside  this compact set, while our approximation is for  functions that are harmonic in a neighborhood of the  compact set. This difference is due to the fact that  in the case of holomorphic functions, we have at our  disposal Mergelyan''s approximation theorem, which  allows such an approximation, while in the case of  harmonic functions, we employ only the classic  approximation theorem of Walsh (harmonic analogue of  the theorem of Runge).\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783838366692\"\u003e\u003ch3\u003eApproximation des fonctions harmoniques par des séries universelles surconvergentes\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783838366692","offer_id":39499082760285,"sku":"9783838366692","price":49.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/5eca59d8-17a6-44b8-b2fe-da260cb71b25.jpg?v=1758875380","url":"https:\/\/shop.autorenwelt.de\/products\/approximation-of-harmonic-functions-by-universal-overconvergent-series-von-innocent-tamptse","provider":"Autorenwelt Shop","version":"1.0","type":"link"}