APPROXIMATION PROPERTIES OF EXPONENTIAL SYSTEMS ON THE REAL LINE AND THE HALF-LINE

For arbitrary a > 0 and alpha > 1 a class of entire functions dependin g on a complex parameter mu is constructed. The values of mu such that the sequence of zeros lambda(n) of a function in this class generates a complete and minimal exponential system exp (-i lambda(n)t - a/t/(a lpha)) in L-P(R) (L-P(R+)), p greater than or equal to 2, are describe d. Examples of such systems were previously known only for alpha = 2.