On random arithmetical functions. I

Let A _Q be the group of complex unit roots of an integer order \( Q \geqslant 2 \). Let \( {\xi_p}\left( {p \in \mathcal{P}} \right) \) be independent random variables distributed uniformly on the set A _Q , where \( \mathcal{P} \)is the set of primes. Let f be a completely multiplicative function defined on \( \mathcal{P} \) by f(p) = ξ _p . We investigate the summatory function of f(n) and the density of those n for which f(n + j) = κ _j (j = 0, …, t), where κ _j ∈ A _Q .     

On arithmetical functions having constant values in some domain

This paper shows that any completely additive complex valued function over a principal configuration in the complex plane, having constant values in some discs, is the identically zero function. In other words, there exists no non-trivial completely additive complex valued function over a principal configuration in  $\mathbb{C}$ which assumes constant values in some domain.     

A characterization of some additive arithmetical functions. V

We give a new characterization of the logarithm as an additive arithmetical function. This revised version was published online in June 2006 with corrections to the Cover Date.     

A characterization of some arithmetical multiplicative functions

Research supported by the Hungarian National Research Foundation No.907.     

On some Hilbert spaces of harmonic functions

Two kinds of spaces of harmonic functions defined on m-dimensional domains are considered. In the first case, the spherical domain is a m-dimensional ball B_r in the second case B_r is replaced by B_r1,r2:=B_r2B_r1. In both cases, several inner products are considered and Hilbert space properties are proved. The reproducing kernel functions of these spaces and hence some new representations for harmonic functions are also obtained     

On spaces of Baire I functions over K-analytic spaces

Suppose that is a relatively countably compact subset of B₁(X), the space of Baire I functions over a K-analytic space X equipped with the pointwise convergence topology. It is proved that (1) the closure of is a strongly countably compact Frechét-Urysohn space; (2) if is ₁ -compact, is a bicompactum; (3) if X is a paracompact space, the closure of is a bicompactum.Translated from Matematicheskie Zametki, Vol. 52, No. 3, pp. 108–116, September, 1992.     

On the zeros of functions from Bergman spaces and some related spaces

We obtain sharp necessary conditions on the counting function of zeros of analytic functions from Bergman spaces with standard weight and from spaces which are their natural generalization.     

On some properties of the functions from Sobolev-Morrey type spaces

In this paper the spaces of type Sobolev-Morrey-W _p,a,г,τ ^l (Q,G)-are constructed, the differential properties are studied and it is proved that the functions from these spaces satisfy Holder's condition, in the case, if the domain G∋R ⁿ satisfies the flexible λ-horn condition.     

Prime-independent arithmetical functions

Summary This paper studies arithmetical functions that are prime-independent and multiplicative. Firstly, it establishes necessary and sufficient conditions for such functions to possess simple formulae relating them to the zeta function. Then it investigates asymptotic average-values and moments of such functions. The results apply to functions of ideals in algebraic numbers fields, or of isomorphism classes in certain categories, as well as to functions of positive integers. Entrata in Redazione il 10 ottobre 1972.