# Toeplitz approach to problems of the uncertainty principle

@inproceedings{Poltoratski2015ToeplitzAT, title={Toeplitz approach to problems of the uncertainty principle}, author={Alexei Poltoratski}, year={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 problem Toeplitz approach to UP Toeplitz version of the Beurling-Malliavin theory Bibliography

## 21 Citations

TOEPLITZ METHODS IN COMPLETENESS AND SPECTRAL PROBLEMS

- MathematicsProceedings of the International Congress of Mathematicians (ICM 2018)
- 2019

We survey recent progress in the gap and type problems of Fourier analysis obtained via the use of Toeplitz operators in spaces of holomorphic functions. We discuss applications of such methods to…

Etudes for the inverse spectral problem

- Mathematics
- 2022

In this note we study inverse spectral problems for canonical Hamiltonian systems, which encompass a broad class of second order differential equations on a half-line. Our goal is to extend the…

Two-spectra theorem with uncertainty

- MathematicsJournal of Spectral Theory
- 2019

The goal of this paper is to combine ideas from the theory of mixed spectral problems for differential operators with new results in the area of the Uncertainty Principle in Harmonic Analysis (UP).…

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…

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…

A Note on multipliers between model spaces

- Mathematics
- 2017

In this note, we study the multipliers from one model space to another. In the case when the corresponding inner functions are meromorphic, we give both necessary and sufficient conditions ensuring…

Mixed data in inverse spectral problems for the Schrödinger operators

- MathematicsJournal of Spectral Theory
- 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…

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…

On the structure of the inverse to Toeplitz-block Toeplitz matrices and of the corresponding polynomial reflection coefficients

- MathematicsTransactions of the American Mathematical Society
- 2019

The results on the inversion of convolution operators as well as Toeplitz (and block Toeplitz) matrices in the 1-D (one-dimensional) case are classical and have numerous applications. We consider the…

## References

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Abstract A classical result by Pál Turán, estimates the global behavior of an exponential polynomial on an interval by its supremum on any arbitrary subinterval. We discuss F. L. Nazarov’s extension…

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Which perturbations of quasianalytic weights preserve quasianalyticity? How to use de Branges’ theorem

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Based on an approach of de Branges and the theory of entire functions, we prove two results pertaining to the Bernstein approximation problem, one concerning analytic perturbations of quasianalytic…