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Archiv der Mathematik

, Volume 72, Issue 3, pp 185–191 | Cite as

On measurable orthogonally exponential functions

  • Janusz Brzdek

Abstract.

Let X be a real linear topological space and \(f:X\rightarrow {\Bbb C}\) satisfy \(f(x+y)=f(x)f(y)\) whenever \(x\perp y\), where \(\perp \subset X^2\) is defined by (01) – (04). We show that if f is universally, Christensen, or Baire measurable (under suitable assumptions on X), then \(f(x)=\exp (A_1(x)+iA_2(x)+cL(x,x))\) for \(x\in X\) with some continuous linear functionals \(A_1,A_2:X\rightarrow {\Bbb R}\), bilinear \(L:X^2\rightarrow {\Bbb R}\), and \(c\in {\Bbb C}\).

Keywords

Exponential Function Topological Space Linear Functional Suitable Assumption Linear Topological Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  • Janusz Brzdek
    • 1
  1. 1.Department of Mathematics, Pedagogical University, Rejtana 16A, PL-35-310 Rzeszów, PolandPL

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