Uniform approximation by polynomials in two functions.
Uniform convergence of power series expansions on the boundary.
Uniqueness theorems
Uniqueness Theorems for Bounded Holomorphic Functions.
Univalence of odd derivatives of even entire functions.
Universal approximation theorem for Dirichlet series.
Universal functions on nonsimply connected domains
We establish certain properties for the class of universal functions in with respect to the center , for certain types of connected non-simply connected domains . In the case where is discrete we prove that this class is -dense in , depends on the center and that the analog of Kahane’s conjecture does not hold.
Universal Taylor series
We strengthen a result of Chui and Parnes and we prove that the set of universal Taylor series is a -dense subset of the space of holomorphic functions defined in the open unit disc. Our result provides the answer to a question stated by S.K. Pichorides concerning the limit set of Taylor series. Moreover, we study some properties of universal Taylor series and show, in particular, that they are trigonometric series in the sense of D. Menchoff.
Universal Taylor series, conformal mappings and boundary behaviour
A holomorphic function on a simply connected domain is said to possess a universal Taylor series about a point in if the partial sums of that series approximate arbitrary polynomials on arbitrary compacta outside (provided only that has connected complement). This paper shows that this property is not conformally invariant, and, in the case where is the unit disc, that such functions have extreme angular boundary behaviour.
Universal Taylor series with maximal cluster sets.
Universally divergent Fourier series via Landau's extremal functions
We prove the existence of functions , the Fourier series of which being universally divergent on countable subsets of . The proof is based on a uniform estimate of the Taylor polynomials of Landau’s extremal functions on .
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Value regions for continued fractions K(a.../1) whose elements lie in parabolic regions.
Vytvořující funkce
Zeros and poles of Dirichlet series
Under certain mild analytic assumptions one obtains a lower bound, essentially of order , for the number of zeros and poles of a Dirichlet series in a disk of radius . A more precise result is also obtained under more restrictive assumptions but still applying to a large class of Dirichlet series.
Zeros of power series and connectedness loci for self-affine sets.
Zeros of Sequences of Partial Sums and Overconvergence
2000 Mathematics Subject Classification: 30B40, 30B10, 30C15, 31A15.We are concerned with overconvergent power series. The main idea is to relate the distribution of the zeros of subsequences of partial sums and the phenomenon of overconvergence. Sufficient conditions for a power series to be overconvergent in terms of the distribution of the zeros of a subsequence are provided, and results of Jentzsch-Szegö type about the asymptotic distribution of the zeros of overconvergent subsequences are stated....
Zeros of the derivatives of entire functions with Hadamard gaps
Zeta functions for the Riemann zeros
A family of Zeta functions built as Dirichlet series over the Riemann zeros are shown to have meromorphic extensions in the whole complex plane, for which numerous analytical features (the polar structures, plus countably many special values) are explicitly displayed.
Zobecnění Taylorova a Laurentova rozvoje