论文标题
两个自由随机变量总和的棕色量度，其中一个是三角形椭圆形
The Brown measure of a sum of two free random variables, one of which is triangular elliptic
论文作者
论文摘要
三角椭圆算子是圆形算子的椭圆形变形的自然扩展。我们获得了三角椭圆算子的总和$ g _ {_ {α，β，γ}} $的棕色度量公式，其带有随机变量$ x_0 $，该$ x_0 $，$ g _ {_ {_ {_ {_ {_ {_ {_ {α，β，β，γ}} $具有与某些Unitial Inalital subalge amalgamation compla。令$ C_T $为圆形操作员。我们证明，$ x_0 + g _ {_ {_ {α，β，γ}} $的棕色度量是$ \ Mathbb {C} $上的明确定义的映射$ x_0 + c_t $的推动量度。我们表明，相对于$ \ mathbb {c} $的lebesgue度量，$ x_0+c_t $的棕色度量绝对是连续的，其密度受$ 1/（π{t}）$界定。这项工作将早期的结果推广到与圆形操作员，半圆形操作员或椭圆操作员为较大类的运算符的添加结果。由于Biane和Voiculescu，我们将操作员值的从属功能扩展到某些无界操作员。这使我们可以将结果扩展到无限的运营商。
The triangular elliptic operators are natural extensions of the elliptic deformation of circular operators. We obtain a Brown measure formula for the sum of a triangular elliptic operator $g_{_{α, β, γ}}$ with a random variable $x_0$, which is $*$-free from $g_{_{α, β, γ}}$ with amalgamation over certain unital subalgebra. Let $c_t$ be a circular operator. We prove that the Brown measure of $x_0 + g_{_{α, β, γ}}$ is the push-forward measure of the Brown measure of $x_0 + c_t$ by an explicitly defined map on $\mathbb{C}$ for some suitable $t$. We show that the Brown measure of $x_0+c_t$ is absolutely continuous with respect to the Lebesgue measure on $\mathbb{C}$ and its density is bounded by $1/(π{t})$. This work generalizes earlier results on the addition with a circular operator, semicircular operator, or elliptic operator to a larger class of operators. We extend operator-valued subordination functions, due to Biane and Voiculescu, to certain unbounded operators. This allows us to extend our results to unbounded operators.
