## 36 Citations

Kernels of Toeplitz operators

- Mathematics
- 2015

Toeplitz operators are met in different fields of mathematics such as stochastic processes, signal theory, completeness problems, operator theory, etc. In applications, spectral and mapping…

Basis properties of complex exponentials and invertibility of Toeplitz operators

- Mathematics
- 2018

We give a criterion for basicity of a sequence of complex exponentials in terms of the invertibility properties of a certain naturally associated Toeplitz operator. The criterion is similar to the…

NSF/CBMS REGIONAL CONFERENCE IN MATHEMATICAL SCIENCES: UNCERTAINTY PRINCIPLES IN HARMONIC ANALYSIS: GAP AND TYPE PROBLEMS Description of Lectures

- Mathematics
- 2012

In the second part of the lecture we discuss connections with spectral problems, starting with the connection to Stationary Gaussian Processes outlined in a classical paper by Krein [21]. We then…

On the chain structure in the de Branges spaces

- Mathematics
- 2021

We study the indivisible intervals and the monotonicity of the growth of the exponential type in the chains of de Branges subspaces in terms of the spectral measure. We prove that for spectral…

Synthesizable differentiation-invariant subspaces

- MathematicsGeometric and Functional Analysis
- 2019

We describe differentiation-invariant subspaces of $${C^\infty(a,b)}$$C∞(a,b) which admit spectral synthesis. This gives a complete answer to a question posed by A. Aleman and B. Korenblum. It turns…

ENTIRE FUNCTIONS AND COMPLETENESS PROBLEMS

- Mathematics
- 2013

In this lecture we continue our discussion of connections with spectral theory for differential operators, started in Lecture 3, in more detail. We will only discuss the case of Schrödinger operators…

## References

SHOWING 1-10 OF 39 REFERENCES

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…

Beurling-Malliavin theory for Toeplitz kernels

- Mathematics
- 2007

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…

On the closure of characters and the zeros of entire functions

- Mathematics
- 1967

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…

Operators, Functions, and Systems: An Easy Reading

- Mathematics
- 2002

Together with the companion volume by the same author, Operators, Functions, and Systems: An Easy Reading. Volume 2: Model Operators and Systems, Mathematical Surveys and Monographs, Vol. 93, AMS,…

Lectures on entire functions

- Mathematics
- 1996

Part I. Entire Functions of Finite Order: Growth of entire functions Main integral formulas for functions analytic in a disk Some applications of the Jensen formula Factorization of entire functions…

On bounded analytic functions

- Mathematics
- 1950

The objective of this paper is to give an alternative derivation of results on bounded analytic functions recently obtained by Ahlfors [1] and Garabedian [2].1 While it is admitted that the main idea…

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…

The Logarithmic Integral

- Mathematics
- 2001

In this chapter we discuss the argument principle and develop several of its consequences. In Section 1 we derive the argument principle from the residue theorem, and we use the argument principle to…

Perspectives in analysis : essays in honor of Lennart Carleson's 75th birthday

- Mathematics
- 2005

The Rosetta Stone of L-Functions.- New Encounters in Combinatorial Number Theory: From the Kakeya Problem to Cryptography.- Perspectives and Challenges to Harmonic Analysis and Geometry in High…

SOME HILBERT SPACES OF ENTIRE FUNCTIONS. II

- Mathematics
- 2010

A Hubert space, whose elements are entire functions, is of especial interest if it has these three properties: (HI). Whenever F(z) is in the Hubert space and has a nonreal zero w, F(z)(z—w)/(z—w) is…