Uniform approximation in the spherical distance by functions meromorphic on Riemann surfaces

详细信息    查看全文

• 作者：P.M. Gauthier^a ; ^{gauthier@dms.umontreal.ca" class="auth_mail" title="E-mail the corresponding author} ; F. Sharifi^b ; ^{fsharif8@uwo.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Approximation ; Riemann surfaces ; Meromorphic approximation ; Chordal metric ; Jordan region
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：445
• 期：2
• 页码：1328-1353
• 全文大小：540 K

文摘

Given a function class="mathmlsrc">class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16303766&_mathId=si1.gif&_user=111111111&_pii=S0022247X16303766&_rdoc=1&_issn=0022247X&md5=fd973ea007c6deca843efc675694b917">class="imgLazyJSB inlineImage" height="18" width="74" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16303766-si1.gif">class="mathContainer hidden">class="mathCode">$f:E\to \bar{\mathbb{C}}$ from a closed subset of a Riemann surface R   to the Riemann sphere class="mathmlsrc">class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16303766&_mathId=si12.gif&_user=111111111&_pii=S0022247X16303766&_rdoc=1&_issn=0022247X&md5=c4b3e40c410b0bcd41003fcca94c19c2">class="imgLazyJSB inlineImage" height="14" width="14" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16303766-si12.gif">class="mathContainer hidden">class="mathCode">$\bar{\mathbb{C}}$, we seek to approximate f in the spherical distance by functions meromorphic on R. As a consequence we generalize a recent extension of Mergelyan's theorem, due to Fragoulopoulou, Nestoridis and Papadoperakis [12]. The problem of approximating by meromorphic functions pole-free on E is equivalent to that of approximating by meromorphic functions zero-free on E, which in turn is related to Voronin's spectacular universality theorem for the Riemann zeta-function.