On indicators of entire functions and extension of solutions of a homogeneous convolution equation

A study is made of the problem of extending solutions of a homogeneous convolution equation generated by analytic functional on convex domains in a multidimensional complex space. Conditions ensuring the simultaneous extension of solutions are given in terms of complete regularity of the growth in limiting directions of accumulations of zeros of the Laplace transform of an analytic functional. These conditions generalize previously known results on this problem. Some properties of indicators of entire functions are also presented.