THE STRING DENSITY-OF-STATES FROM THE CONVOLUTION THEOREM

We study the microcanonical density of states and the thermal properti es of a bosonic string gas starting from a calculation of the Helmholt z free energy in the S-representation. By adding more and more strings to the single string system, we induce that, for infinite volume, the re is no negative specific heat region but a transition at a finite va lue of the energy per string from the low energy regime to a region of infinite specific heat at the Hagedorn temperature. Forcing the descr iption of this phase in terms of strings gives a picture in which ther e is a very fat string in a sea of low energetic ones. We argue that t he necessary changing of this description should not change the fact t hat perturbatively T-H is a maximum temperature of the system. (C) 199 7 Elsevier Science B.V.