T] is rd-continuous and [tau](*), a(*), c(*) are defined on T and denote nonnegative, rd-continuous bounded functions and

T] is rd-continuous and [tau](*), a(*), b(*) are defined on T and denote nonnegative, rd-continuous bounded functions and

Suppose the function f is [GAMMA]-sublinear affine on (a,b), with [GAMMA](x)

bounded function.

i) For all bounded functions [epsilon] : S x T [right arrow] C the pointwise product [epsilon][psi] is in V(S, T).

infinity]] (S) the space of all complex valued bounded functions on S, equipped with the sup-norm.

n](k; [square root of 2n + 1]) is a sequence of uniformly

bounded functions that converges almost uniformly to the ideal window with bandwidth 2.

We set a binary operation in the space of

bounded functions on a compact interval B (I ) (although the construction can be done in the space of measurable essentially bounded mappings L "(I ) as well).

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.

GOLUZIN, some estimates for

bounded functions (Russian), Mat.

We denote by C(R) the space of all uniformly continuous and

bounded functions f: R [right arrow] R (or f: R [right arrow] C) endowed with the usual sup-norm [parallel] * [parallel] C(R) [equivalent ot] [parallel] [parallel][infinity], and by [C.