Questionable notation page 176

Perhaps a little pedantic, but in the definitions of

and

on p.176, the left-hand sides are functions of

x, while the right-hand sides are functions of

z.

I understand that the LHS domains are restricted to the real line, while the two components of the hyperfunction have domains that are the top and bottom halves of the complex plane respectively... but it still looks wrong to me.

Unless of course, it were to be stated explicitly that

. But it wasn't.