Uniform boundedness of the derivatives of meromorphic inner functions on the real line

@article{Rupam2013UniformBO,
  title={Uniform boundedness of the derivatives of meromorphic inner functions on the real line},
  author={Rishika Rupam},
  journal={Journal d'Analyse Math{\'e}matique},
  year={2013},
  volume={131},
  pages={189-206}
}
  • Rishika Rupam
  • Published 26 September 2013
  • Mathematics
  • Journal d'Analyse Mathématique
Inner functions are an important and popular object of study in the field of complex function theory. We look at meromorphic inner functions with a given spectrum and provide sufficient conditions for them to have uniformly bounded derivative on the real line. This question was first studied by Louis de Branges in 1968 and was later revived by Anton Baranov in 2011. 
View on Springer
arxiv.org
3 Citations
Background Citations
2

3 Citations

Citation Type

Citation Type

Restricted interpolation by meromorphic inner functions
Abstract Meromorphic Inner Functions (MIFs) on the upper half plane play an important role in applications to spectral problems for differential operators. In this paper, we survey some recent…
Uniqueness theorems for meromorphic inner functions
We prove some uniqueness problems for meromorphic inner functions on the upper half-plane. In these problems we consider spectral data depending partially or fully on the spectrum, derivative values…
O ct 2 02 1 UNIQUENESS THEOREMS FOR MEROMORPHIC INNER FUNCTIONS
  • Mathematics
  • 2021
We prove some uniqueness problems for meromorphic inner functions on the upper half-plane. In these problems we consider spectral data depending partially or fully on the spectrum, derivative values…

References

SHOWING 1-9 OF 9 REFERENCES
Meromorphic Inner Functions, Toeplitz Kernels and the Uncertainty Principle
This paper touches upon several traditional topics of 1D linear complex analysis including distribution of zeros of entire functions, completeness problem for complex exponentials and for other…
On the closure of characters and the zeros of entire functions
The problem to be studied in this paper concerns the closure properties on an interval of a set of characters {e~nx}~, where A = {2n}~ is a given set of real or complex numbers without finite point…
Completeness and Riesz bases of reproducing kernels in model subspaces
We use the recent approach of N. Makarov and A. Poltoratski to give a criterion of completeness of systems of reproducing kernels in the model subspaces KΘ = H 2aΘH2 of the Hardy class H. As an…
Polya sequences, Toeplitz kernels and gap theorems
Beurling-Malliavin theory for Toeplitz kernels
AbstractWe consider the family of Toeplitz operators $T_{J\bar{S}^{a}}$ acting in the Hardy space H2 in the upper halfplane; J and S are given meromorphic inner functions, and a is a real…
Admissible Majorants for Model Subspaces of H 2, Part I: Slow Winding of the Generating Inner Function
Abstract A model subspace ${{K}_{\Theta }}$ of the Hardy space ${{H}^{2}}={{H}^{2}}\left( {{\mathbb{C}}_{+}} \right)$ for the upper half plane ${{\mathbb{C}}_{+}}$ is ${{H}^{2}}\left(…
Hilbert spaces of entire functions
Recent Advances in Operator-Related Function Theory
Admissible majorants for model subspaces of H 2 , Part I : Slow winding of the generating inner function , Canad
  • J . Math . Vol .
  • 2003