I cant find any definition on $\alpha(n)$ , and somthing in Neharis paper -57 on bilinear forms confuses me ;( https://www.jstor.org/stable/1969670?seq=1#fndtn-page_scan_tab_contents) .
He starts of stating "Theorem 1" in terms of $\alpha(n)=\int F(\theta)e^{-in \theta}$ but at a later point he writes $\alpha(n)=\int F(\theta)e^{in \theta}$ and refers to the same numbers as negative coefficients and from what I can tell the same function $F$. I looked in Hardy's book "Inequalities" and cant find a definiton of $\alpha(n)$ there either. I knew it was possible to consider fourier coefficets with different scalars and that this could cause trouble but could we define them with "opposite" signs aswell?
Anyway, my question is what does Nehari mean by $\alpha(n)$ or why donst he care about the distinction?
Update; I thought about this, any sequence of "nonpostive fourier coeff." is the fourier coeff. for some other function, maybe he just flips them over? But that would be a different $F$..? Therefore a statement regarding "some" $F$ would still be vaild I think.