Fundamental Solutions for the Tangential Cauchy–Riemann Complex on a Convex Hypersurface

2017 ◽  
pp. 312-326
Author(s):  
Albert Boggess
Keyword(s):  
Fundamental Solutions ◽  
Convex Hypersurface ◽  
Cauchy Riemann

Universal Series on a Riemann Surface

2011 ◽  
Vol 63 (5) ◽  
pp. 1025-1037
Author(s):  
Raphäel Clouâtre
Keyword(s):  
Riemann Surface ◽  
Holomorphic Function ◽  
Compact Subset ◽  
Fundamental Solutions ◽  
Partial Sums ◽  
Universal Series ◽  
Cauchy Riemann ◽  
Series Of Functions

Abstract Every holomorphic function on a compact subset of a Riemann surface can be uniformly approximated by partial sums of a given series of functions. Those functions behave locally like the classical fundamental solutions of the Cauchy–Riemann operator in the plane.

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