| Abstract [eng] |
Lets=+ibe a complex variable, and,0< 1, be a fixed parameter. The Riemannand Hurwitz zeta - functions(s)and(s;)are defined, for >1, by the series(s) =1Xm=11msand(s;) =1Xm=01(m+)s;and were meromorphically continued to the whole complex plane.It is known that functions(s)and(s;)are universal in the sence of that, their shifts(s+i)and(s+i;)approximate every analytic function. H. Mishou proved joint universality theoremon the approximation of a pair of analytic functions by shifts((s+i);(s+i;)).In the masters degree work, we consider the universality of composite functionsF((s);(s;))for some operators F. LetD=fs2C:12< <1g,H(D)be the square of analytic functions onDequipped with the topology of uniform convergence on compact. LetKbe the class of compactsubsets of the stripDwith conected complements, and letH(K),K2K, be the class of continuosfunctions onKwhich are analytic in the interior ofK. |
