I recently came across an equation which says: $$\alpha_0+\alpha_1y^{*\beta_1}+\alpha_2\left(y-c\right)^{*\beta_2}+\alpha_3\left(y-1\right)^{*\beta_3}$$ $$=\alpha_0+\alpha_1y^{\beta_1}+\alpha_2\left(y-c\right)^{*\beta_2}-\alpha_3\left(1-y\right)^{\beta_3}$$ where all the parameters are real, $0<y<1$ and $0<c<1$
What does $(y-c)^{*\beta}$ mean? How is it different than $(y-c)^{\beta}$?
Is it that $\alpha_2\left(y-c\right)^{*\beta_2}$ is a piecewise function?
This was seen in this literature on XGLD
See definition 1 (8) in page 4. Is a piecewise function and it is different because it remains in $\mathbb{R}$. Consider $\beta = 1/2,y=0,c=1$, then $(y-c)^{\beta}=(-1)^{1/2}=i$ but $(y-c)^{*\beta}=-|0-1|^{1/2}=-1$.