-valent meromorphic functions with alternating coefficients based on integral operator.
Painlevé's problem and analytic capacity.
In this paper we survey some recent results in connection with the so called Painlevé's problem and the semiadditivity of analytic capacity γ. In particular, we give the detailed proof of the semiadditivity of the capacity γ+, and we show almost completely all the arguments for the proof of the comparability between γ and γ+.
Pairs of paths and critical points.
Partial sums of certain analytic and univalent functions.
Partial sums of certain analytic functions.
Partial sums of certain meromorphic functions.
Partial sums of certain meromorphic -valent functions.
Partial sums of functions of bounded turning.
Partial sums of functions of bounded turning.
Partial sums of some meromorphic functions.
Partial sums of Taylor series on a circle
We characterize the power series with the geometric property that, for sufficiently many points , , a circle contains infinitely many partial sums. We show that is a rational function of special type; more precisely, there are and , such that, the sequence , , is periodic. This result answers in the affirmative a question of J.-P. Kahane and furnishes stronger versions of the main results of [Katsoprinakis, Arkiv for Matematik]. We are led to consider special families of circles with...
Pathwise connectivity in uniform domains with small exceptional sets.
Periodic quasiregular mappings of finite order.
The authors construct a periodic quasiregular function of any finite order p, 1 < p < infinity. This completes earlier work of O. Martio and U. Srebro.
Perturbative computation of analytic invariants of resonant diffeomorphisms of
Phragmén-Lindelöf theorems for subharmonic functions on the unit disk.
Pick-Nevanlinna interpolation on finitely-connected domains
Let Ω be a domain in the complex plane bounded by m+1 disjoint, analytic simple closed curves and let be n+1 distinct points in Ω. We show that for each (n+1)-tuple of complex numbers, there is a unique analytic function B such that: (a) B is continuous on the closure of Ω and has constant modulus on each component of the boundary of Ω; (b) B has n or fewer zeros in Ω; and (c) , 0 ≤ j ≤ n.
Planar harmonic univalent and related mappings.
Plücker relations for p(e...).
Point estimation and the convergence of the Ehrlich-Aberth method.
Point shift differentials and extremal quasiconformal mappings.