1 citations · 1 across the 8 of their papers we have counts for
9 papers
An affirmative answer to a problem of Cater
Arthur A. Danielyan
Does there exist an increasing absolutely continuous function, such that is both countable and dense? This problem was proposed by…
On a problem of von Renteln
Arthur A. Danielyan
We discuss the solution of a harmonic analysis problem proposed by M. von Renteln in 1980.
On a boundary property of Blaschke products
Arthur Danielyan, Spyros Pasias
A Blaschke product has no radial limits on a subset of the unit circle but has unrestricted limit at each point of if and only if is a closed set of mea…
A proof of Fatou's interpolation theorem
Arthur A. Danielyan
For Fatou's interpolation theorem of 1906 we suggest a new elementary proof.
Radial limits and boundary uniqueness
Arthur A. Danielyan
The paper sheds a new light on the fundamental theorems of complex analysis due to P. Fatou, F. and M. Riesz, N. N. Lusin, I. I. Privalov, and A. Beurling. Only classical tools ava…
Rubel's problem on bounded analytic functions
Arthur A. Danielyan
The paper shows that for any set of Lebesgue measure zero on the unit circle there exists a function such that the radial limits of exist at ea…
Fatou's interpolation theorem implies the Rudin-Carleson theorem
Arthur A. Danielyan
The purpose of this paper is to show that the Rudin-Carleson interpolation theorem is a direct corollary of Fatou's much older interpolation theorem (of 1906).
On the zero-free polynomial approximation problem
Arthur A. Danielyan
Let be a compact set in with connected complement, and let be the class of all complex continuous function on that are analytic in the interior of…
Weak-star convergence and a polynomial approximation problem
Arthur A. Danielyan
Let be an arbitrary subset of the unit circle and let be a function defined on . When there exist polynomials which are uniformly bounded by a number o…