MathDB

7

Part of 1977 Miklós Schweitzer

Problems(1)

Miklos Schweitzer 1977_7

Source: locally compact solvable group+complex numbers+complex-valued functions

1/25/2009
Let G G be a locally compact solvable group, let c1,…,cn c_1,\ldots, c_n be complex numbers, and assume that the complex-valued functions f f and g g on G G satisfy ∑k=1nckf(xyk)=f(x)g(y)  for all  x,y∈G  . \sum_{k=1}^n c_k f(xy^k)=f(x)g(y) \;\textrm{for all} \;x,y \in G \ \ . Prove that if f f is a bounded function and inf⁡x∈GRef(x)χ(x)>0 \inf_{x \in G} \textrm{Re} f(x) \chi(x) >0 for some continuous (complex) character χ \chi of G G, then g g is continuous. L. Szekelyhidi
functiongroup theoryGalois Theorycomplex numberscomplex analysiscomplex analysis unsolved