02/27/2021, 11:37 AM
I agree with Tommy. That kind of functional equation is structurally analogous to double recursion. I wonder if it is possible to adapt, at least theoretically disregarding radii of convergence, the classic and Nixon's limit formulas to that cases. The problem that I see, as Tommy does, that thing going back tho the successor as the limits goes to infinity. There has to be a deep reason for this. In superfunctions/subfunctions and non-integer-superfunctions (aka non-integer ranks) successor is a fixed point of the "operator".
The iteration theory of those kinds of (non-linear)operators on functions spaces has to coincide with the rank theory of the underlying function spaces. As different generating laws define different HOF(amilies) and in some cases a generating law is in some cases a kind of operator on functions, ranks theory reduces to a special kind of iteration theory.
The iteration theory of those kinds of (non-linear)operators on functions spaces has to coincide with the rank theory of the underlying function spaces. As different generating laws define different HOF(amilies) and in some cases a generating law is in some cases a kind of operator on functions, ranks theory reduces to a special kind of iteration theory.
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)
