Proof of US hegemony and its decline?

In discussions with colleagues who are less persuaded than I am by some of
the world systems litertature, I have recently been presented with several
questions that I think raise some interesting problems. Regardless of my own
readings in world systems analysis, I do not think of myself as an expert,
and so I want to invite comments and/or references to literature.

First, one commented with reference to recent articles by Wallerstein on the
FBC website, what Wallerstein does is to stipulate that American hegemony is
in decline, rather than to demonstrate it.

Secondly, in a twist on this, one asked: was the US ever hegemonic? It
surely has been dominant in many fields, but is dominance the same as
hegemony?

Thirdly, and I think this is where I began to find the issues more tricky,
if dominance = hegemony, then the US certainly is dominant in military terms
at least, and not exactly at the bottom of the food chain in economic terms.

In all of these comments, I sensed that there was worry over
counter-triumphalist triumphalism, of proclaiming the end of US hegemony or
the end of capitalism (the two not necessarily the same), well before time,
or in denial of evidence to the contrary.

Many thanks and best wishes,

Max.