Treatment of Gamow states, using tempered ultradistributions

In the present manuscript, and with the use of tempered ultradistributions, we extend analitically the pseudonorm of Gamow states as defined originall y by T. Berggren. We define this pseudonorm for all states determined by th e zeros of the Jest function for any short range potential. As a particular example we study the s-states corresponding to the square-well potential.