Möbius’s functional equation and Schur’s lemma with applications to the complex unit disk
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DOI: 10.1007/s00010-016-0452-9
Abstract: Möbius addition is defined on the complex open unit disk by $$\begin{aligned} a\oplus _M b = \dfrac{a+b}{1+\bar{a}b} \end{aligned}$$a⊕Mb=a+b1+a¯band Möbius’s exponential equation takes the form $$L(a\oplus _M b) = L(a)L(b)$$L(a⊕Mb)=L(a)L(b), where L is a complex-valued function… read more here.
Keywords: equation; complex unit; unit disk; exponential equation ... See more keywords