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Integral representations of bounded starlike functions

Frode Rønning (1995)

Annales Polonici Mathematici

For α ≥ 0 let $ℱ_{α}$ denote the class of functions defined for |z| < 1 by integrating $1 / {(1 - x z)}^{α}$ if α > 0, and log(1/(1-xz)) if α = 0, against a complex measure on |x| = 1. We study families of starlike functions where zf’(z)/f(z) ranges over a parabola with given focus and vertex. We prove a number of properties of these functions, among others that they are bounded and that they belong to $ℱ_{0}$ . In general, it is only known that bounded starlike functions belong to $ℱ_{α}$ for α > 0.

Integrals of the Cauchy type

Josef Král, Jaroslav Lukeš (1972)

Czechoslovak Mathematical Journal

Integrated Design of an Active Flow Control System Using a Time-Dependent Adjoint Method

E.J. Nielsen, W.T. Jones (2011)

Mathematical Modelling of Natural Phenomena

An exploratory study is performed to investigate the use of a time-dependent discrete adjoint methodology for design optimization of a high-lift wing configuration augmented with an active flow control system. The location and blowing parameters associated with a series of jet actuation orifices are used as design variables. In addition, a geometric parameterization scheme is developed to provide a compact set of design variables describing the wing...

Interpolación en espacios de funciones armónicas con desarrollos asintóticos.

Gaspar Mora Martínez (1989)

Collectanea Mathematica

The article puts up the problem of finding harmonic functions on a domain D, which for simplicity is a disk with the origin as a boundary point, continuous on D, and with arbitrary asymptotic harmonic expansion. To solve it, in the space Ac(D) of harmonic functions on D, continuous on D and with aymptotic harmonic expansion at 0, we define the topology Tc for which it is a Fréchet space. There we define the linear functionals which map each function to the coefficients of its asymptotic harmonic...

Interpolating sequences and the Nevanlinna Pick problem.

Arne Stray (1991)

Publicacions Matemàtiques

The extremal solutions to the Nevanlinna Pick problem are studied. If there is more than one solution, Nevanlinna showed that all extremal solutions are inner functions. With some extra information on the interpolation data we find that the extremal solutions are Blaschke products whose zeroes form a finite union of interpolating sequences.

Interpolating sequences in the unit ball of $C^{n}$

N. Pandeski (1985)

Matematički Vesnik

Interpolation and Frames in Certain Banach Spaces of Entire Functions.

Robert M. Young (1997)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

Interpolation by multipliers on certain spaces of analytic functions.

Mosaleheh, K., Seddighi, K. (2000)

International Journal of Mathematics and Mathematical Sciences

Interpolation from a subset of the boundary

D. R. Georgijević (1988)

Matematički Vesnik

Interpolation of bounded sequences

Francesc Tugores (2010)

Czechoslovak Mathematical Journal

This paper deals with an interpolation problem in the open unit disc $𝔻$ of the complex plane. We characterize the sequences in a Stolz angle of $𝔻$ , verifying that the bounded sequences are interpolated on them by a certain class of not bounded holomorphic functions on $𝔻$ , but very close to the bounded ones. We prove that these interpolating sequences are also uniformly separated, as in the case of the interpolation by bounded holomorphic functions.

Interpolation of entire functions on regular sparse sets and $q$ -Taylor series

Michael Welter (2005)

Journal de Théorie des Nombres de Bordeaux

We give a pure complex variable proof of a theorem by Ismail and Stanton and apply this result in the field of integer-valued entire functions. Our proof rests on a very general interpolation result for entire functions.

Interpolation of infinite order entire functions.

Robert E. Heyman (1994)

Revista Matemática Iberoamericana

Interpolation operators on the space of holomorphic functions on the unit circle

Josef Kofroň (2001)

Applications of Mathematics

The aim of the paper is to get an estimation of the error of the general interpolation rule for functions which are real valued on the interval $[- a, a]$ , $a \in (0, 1)$ , have a holomorphic extension on the unit circle and are quadratic integrable on the boundary of it. The obtained estimate does not depend on the derivatives of the function to be interpolated. The optimal interpolation formula with mutually different nodes is constructed and an error estimate as well as the rate of convergence are obtained. The general...

Invariant subspaces on open Riemann surfaces

Morisuke Hasumi (1974)

Annales de l'institut Fourier

Let $R$ be a hyperbolic Riemann surface, $d_{χ}$ a harmonic measure supported on the Martin boundary of $R$ , and $H^{\infty} (d χ)$ the subalgebra of $L^{\infty} (d χ)$ consisting of the boundary values of bounded analytic functions on $R$ . This paper gives a complete classification of the closed $H^{\infty} (d χ)$ -submodules of $L^{p} (d χ)$ , $1 \leq p \leq \infty$ (weakly $^{*}$ closed, if $p = \infty$ , when $R$ is regular and admits a sufficiently large family of bounded multiplicative analytic functions satisfying an approximation condition. It also gives, as a corollary, a corresponding result for the Hardy...

Invariant subspaces on open Riemann surfaces. II

Morisuke Hasumi (1976)