Suppose the function f is [GAMMA]-sublinear affine on (a,b), with [GAMMA](x) bounded function
A more general low-pass filter M is given by a complex-valued, bounded function
v] (t) is a bounded function
on (0,[infinity]) also shows that in the case v [greater than or equal to] -1/2, [[phi].
Let U be the class of analytic bounded functions
of the form
b](X) is contained in the uniform closure of F-simple functions on X in the space of all bounded functions
on X and so each f [member of] [C.
infinity]](X): the set of all bounded functions
like f : X [right arrow] C [2, Chapter 6] where X has more than one element.
1) The connections between bandlimited functions and exponentially bounded functions
are going back to the famous Paley-Wiener theorem.