Local analytic solutions of a functional equation

• Main Authors: Andrzej Smajdor, Wilhelmina Smajdor
• Format: Article
• Language: deu
• Published: Wydawnictwo Naukowe Uniwersytetu Pedagogicznego 2004-05-01
• Series: Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica
• Online Access: http://studmath.up.krakow.pl/index.php/studmath/article/view/26
• ISSN: 2081-545X

All analytic solutions of the functional equation
 [
 |f(rexp(iheta))|^{2}+|f(1)|^{2}=|f(r)|^{2}+|f(exp(iheta))|^{2}
 ]
 in the annulus
 [
 P:={zin mathbb{C}: 1-epsilonle|z|le1+epsilon} 
 ]
 and in the domain
 [
 D:={z=re^{iheta}in mathbb{C}: 1-epsilonle r le 1+epsilon, hetain (-delta,delta)},
 ]
 are found.