Toeplitz approach to problems of the uncertainty principle

  title={Toeplitz approach to problems of the uncertainty principle},
  author={Alexei Poltoratski},
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 
Toeplitz order
  • A. Poltoratski
  • Mathematics
    Proceedings 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
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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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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
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Mixed data in inverse spectral problems for the Schrödinger operators
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
  • 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
  • A. Sakhnovich
  • Mathematics
    Transactions 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


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1 Local estimates of exponential polynomials and their applications to inequalities of uncertainty principle type-part I after
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