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.
Point Systems with Extremal Properties and Conformal Mapping.
Pointwise inequalities of logarithmic type in Hardy-Hölder spaces
We prove some optimal logarithmic estimates in the Hardy space with Hölder regularity, where is the open unit disk or an annular domain of . These estimates extend the results established by S. Chaabane and I. Feki in the Hardy-Sobolev space of the unit disk and those of I. Feki in the case of an annular domain. The proofs are based on a variant of Hardy-Landau-Littlewood inequality for Hölder functions. As an application of these estimates, we study the stability of both the Cauchy problem...
Polarization, conformal invariants and Brownian motion.
Polya's theorem for non-entire functions
Polynômes à coefficients unimodulaires sur le cercle unité
Polynômes quadratiques et attracteur de Hénon
Polynomial Growth along Jordan Arcs.
Polynomials of Maximal Index.
Polynomials, sign patterns and Descartes' rule of signs
By Descartes’ rule of signs, a real degree polynomial with all nonvanishing coefficients with sign changes and sign preservations in the sequence of its coefficients () has positive and negative roots, where and . For , for every possible choice of the sequence of signs of coefficients of (called sign pattern) and for every pair satisfying these conditions there exists a polynomial with exactly positive and exactly negative roots (all of them simple). For this is not...