Based on the concept of so-called (total) omnipresence of operators, several results on the generity of (translation-dilation)
universal functions are proved. Mainly to have a unified approach to holomorphic and harmonic functions, in the first part
operators on spaces of P-holomorphic functions are considered. The second part is devoted to holomorphic functions having lacunary power series structure
and to holomorphic functions which are univalent in certain prescribed sets.
Если функция u(x) = u(x1…, xn) имеет в точке x0 второй асимптотический дифференциал, след матрицы квадратичной формы которого равен нулю, то u(x) наэывается асимптотически гармонической в точке x0. В работе докаэана гармоничность суммируемых асимптотически гармонических функций.
A. Beurling introduced harmonic functions attached to measurable functions satisfying suitable conditions and defined their
spectral sets. The concept of spectral sets is closely related to approximations by trigonometric polynomials. In this paper
we consider spectral sets of the harmonic functions attached to the Riemann zeta-function and its modification.