PROBABILITY AND ESTIMATES OF WIMON-VALIRON TYPE FOR THE EVOLUTIONS EQUATIONS

By virture of a classical results of Wimon and Vakiron the maximum modulus M(r) of an entice functions is related to the maximum term µ(r) of this power series by the relation M(r)<µ(r) (logµ(r)) 1/2+ε, ε>0 which is satisfied outside of an set of finite loqarithmic measore- Applying estimations (for t → 0 or t →∞) for the solution of the differential equations of the from in Hilbert space, where A (t) is a linear operator with discrete spectrum. Particulary, from known results of author follow, that for example, for the solutions of frist initial value, problem with homogemues boundary condition for the inverse heat operator.