2001 jeep Cherokee sport rpms die down then shuts off when you're not touching the gas after touching the gas for the 1st time after starting does idle after start especially after warming up?

It could be the jeep needs a tune up, but let's assume that this is not the case. I would suggest starting with the fuel filter, if this is not the case I would next replace the t.p.s.(throttle positioning sensor) Chrysler products seem to have trouble with this item.