Remarks on restricted Nevanlinna transforms

Demonstratio mathematica

article

Lech Jankowski¹  Zbigniew J. Jurek¹ 

[1] Institute of Mathematics, University of Wrocław

关键词: Nevanlinna transform;    self-energy functional;    Fourier and Laplace transforms;    free additive Voiculescu convolution;    boolean infinitely divisible measures;   

DOI  :  10.1515/dema-2013-0384

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

The Nevalinna transform K a , ρ ( z ) of a positive measure ρ and a constant a , plays an important role in complex analysis and – more recently – in the context of the boolean convolution. We show here that its restriction to the imaginary axis, k a , ρ ( it ), can be expressed as the Laplace transform of the Fourier transform (a characteristic function) of ρ . Consequently, k a ρ is sufficient for the unique identification of the measure ρ and the constant a . Finally, we identify a relation between the free additive Voiculescu ⊞ and boolean ⊎ convolutions.

【 授权许可】

CC BY