# Uniqueness theorems for meromorphic inner functions

@inproceedings{Hatinouglu2021UniquenessTF, title={Uniqueness theorems for meromorphic inner functions}, author={Burak Hatinouglu}, year={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 at the spectrum, Clark measure or the spectrum of the negative of a meromorphic inner function.

## References

SHOWING 1-10 OF 22 REFERENCES

Restricted interpolation by meromorphic inner functions

- Mathematics
- 2016

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…

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

- Mathematics
- 2013

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…

Meromorphic Inner Functions, Toeplitz Kernels and the Uncertainty Principle

- Mathematics
- 2005

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 determinacy problem for measures

- Mathematics
- 2015

We study the general moment problem for measures on the real line, with polynomials replaced by more general spaces of entire functions. As a particular case, we describe measures that are uniquely…

Bernstein’s Problem on Weighted Polynomial Approximation

- Mathematics
- 2015

We formulate a necessary and sufficient condition for polynomials to be dense in a space of continuous functions on the real line, with respect to Bernstein’s weighted uniform norm. Equivalently, for…

Mixed data in inverse spectral problems for the Schrödinger operators

- Mathematics, Physics
- 2019

We consider the Schr\"{o}dinger operator on a finite interval with an $L^1$-potential. We prove that the potential can be uniquely recovered from one spectrum and subsets of another spectrum and…

Spectral gaps for sets and measures

- Mathematics
- 2009

If X is a closed subset of the real line, denote by GX the supremum of the size of the gap in the Fourier spectrum of a measure, taken over all non-trivial finite complex measures supported on X. In…

De Branges functions of Schroedinger equations

- Mathematics
- 2015

We characterize the Hermite–Biehler (de Branges) functions E which correspond to Schroedinger operators with $$L^2$$L2 potential on the finite interval. From this characterization one can easily…

Toeplitz approach to problems of the uncertainty principle

- Mathematics
- 2015

Mathematical shapes of uncertainty Gap theorems A problem by Polya and Levinson Determinacy of measures and oscillations of high-pass signals Beurling-Malliavin and Bernstein's problems The type…

Polya sequences, Toeplitz kernels and gap theorems

- Mathematics
- 2009

A separated sequence $\Lambda$ on the real line is called a Polya sequence if any entire function of zero exponential type bounded on $\Lambda$ is constant. In this paper we solve the problem by…