arXiv subjects
Publications and source records attributed to Lech Jankowski.
We explain the appearance of the free compression of a transition measure in the problem of the restriction of the representation of the symmetric group to a subgroup by showing the responsible free projection.
We explain the appearance of free convolution of Kerov transition measures in the outer product of representations of S_n by showing that some elements of the group algebra are asymptotically free.
The Nevanlinna transform K(z), of a measure and a real constant, plays an important role in the complex analysis and more recently in the free probability theory (boolean convolution). It is shown that its restriction k(it) (the restricted Nevanlinna transform) to the imaginary axis can be expressed as the Laplace transform of the Fourier transform (characteristic function) of the corresponding measure. Finally, a relation between the Voiculescu and the boolean convolution is indicated.