Partially defined semigroups relative to multiplicative free convolution

110 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

On a remarkable semigroup of homomorphisms with respect to free multiplicative convolution (2007, background): “7 of [5] that μ⊞t+1 has a nonzero absolutely continuous part for any t > 0 if and only if μ is not concentrated in one point.”
Eigenvalues of non-hermitian random matrices and Brown measure of non-normal operators: hermitian reduction and linearization method (2015, background): “1 v −Fμ a2 ( 1 v ) is known [4] to be injective, in fact strictly increasing whe never”
The arithmetic of distributions in free probability theory (2005, methodology): “Note thatBercovici and Belinschi [8] gave a related approach using other analytic methods.”
Lectures on the Combinatorics of Free Probability (2006, background): “For analytic properties of the semigroup (μ )t≥1 see [5]; for a version for multiplicative free convolution see [6].”