Universal series induced by approximate identities and some relevant applications

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• 作者：Vassili  ; Nestoridis^a ;   ; ^{vnestor@math.uoa.gr} ; Sebastian  ; Schmutzhard^b ;   ; ^{sebastian.schmutzhard@univie.ac.at} ; Vangelis  ; Stefanopoulos^c ;   ; ^{vstefan@aegean.gr}
• 关键词：Universal series ; Wiener algebra ; Approximation to the identity ; Gauss kernel ; Poisson kernel ; Normal distribution ; Heat equation ; Laplace&rsquo ; s equation
• 刊名：Journal of Approximation Theory
• 出版年：2011
• 出版时间：December 2011
• 年：2011
• 卷：163
• 期：12
• 页码：1783-1797
• 全文大小：239 K

文摘

We prove the existence of series , whose coefficients are in and whose terms are translates by rational vectors in of a family of approximations to the identity, having the property that the partial sums are dense in various spaces of functions such as Wiener¡¯s algebra , , , , for every , and the space of measurable functions. Applying this theory to particular situations, we establish approximations by such series to solutions of the heat and Laplace equations as well as to probability density functions.