# Restricted interpolation by meromorphic inner functions

@article{Poltoratski2016RestrictedIB, title={Restricted interpolation by meromorphic inner functions}, author={Alexei Poltoratski and Rishika Rupam}, journal={Concrete Operators}, year={2016}, volume={3}, pages={102 - 111} }

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 results concerning function theoretic properties of MIFs and show their connections with spectral problems for the Schrödinger operator.

## 2 Citations

Uniqueness theorems for meromorphic inner functions

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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…

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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 1-10 OF 53 REFERENCES

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…

Inner functions and related spaces of pseudocontinuable functions

- Mathematics
- 1993

Let θ be an inner function, let α ∈ C, ¦α¦=1. Then the harmonic function ℜ[(α+θ)]/(α−θ)] is the Poisson integral of a singular measureσα D. N. Clark's known theorem enables us to identify in a…

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…

Inverse spectral problems and closed exponential systems

- Mathematics
- 2005

Consider the inverse eigenvalue problem of the Schr?odinger operator de- fined on a finite interval. We give optimal and almost optimal conditions for a set of eigenvalues to determine the…

Aleksandrov-Clark measures and semigroups of analytic functions in the unit disc

- Mathematics
- 2007

In this paper we prove a formula describing the infinitesimal generator of a contin- uous semigroup ('t) of holomorphic self-maps of the unit disc with respect to a boundary regular fixed point. The…

Isometric embeddings of coinvariant subspaces of the shift operator

- Mathematics
- 1998

AbstractLet θ be an inner function. The main aim of this paper is to describe all positive measures on the unit circle
$$\mathbb{T}$$
such that
$$\int\limits_\mathbb{T} {\left| f \right|^2 } d\mu =…

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…

AN INVERSE STURM-LIOUVILLE PROBLEM WITH MIXED GIVEN DATA*

- Mathematics
- 1978

In general the potential function $q( x )$ in a Sturm–Liouville problem is uniquely determined by two spectra. It is shown here that if $q( x )$ is prescribed over the interval $\left(…