One cannot hear the winding number
Jean Bourgain,Gady Kozma +1 more
TLDR
In this article, an example of two continuous maps f and g of the circle to itself with the same absolute value of the Fourier transform but with different winding numbers, answering a question of Brezis is given.Abstract:
We construct an example of two continuous maps f and g of the circle to itself with the same absolute value of the Fourier transform but with different winding numbers, answering a question of Brezis.read more
Citations
More filters
Journal ArticleDOI
Szegö's theorem and its probabilistic descendants
N. H. Bingham,London +1 more
TL;DR: The theory of orthogonal polynomials on the unit circle (OPUC) dates back to Szego's work of 1915-21, and has been given a great impetus by the recent work of Simon, in particular his survey paper and three recent books.
Posted Content
Szeg\"o's Theorem and its Probabilistic Descendants
TL;DR: The theory of orthogonal polynomials on the unit circle (OPUC) dates back to Szeg\"o's work of 1915-21, and has been given a great impetus by the recent work of Simon as discussed by the authors.
Journal ArticleDOI
Estimates for the topological degree and related topics
Abstract: This is a survey paper on estimates for the topological degree and related topics which range from the characterizations of Sobolev spaces and BV functions to the Jacobian determinant and nonlocal filter problems in Image Processing. These results are obtained jointly with Bourgain and Brezis. Several open questions are mentioned.
Journal ArticleDOI
Geometric significance of Toeplitz kernels
TL;DR: In this article, it was shown that the injectivity problem for Toeplitz operators is linked to the existence of geodesics in the Grassmann manifold of L 2.
Posted Content
Complex derivatives are continuous - three self-contained proofs. Part 1
TL;DR: In this article, the basic fact of analysis that complex derivatives are continuous has been proved in three ways: the first, classical, proof of Cauchy and Goursat using integration, the second proof of Whyburn and Connell using the winding number, and the third proof of Adel'son-Vel'skii and Kronrod employing graphs of real bivariate functions.
References
More filters
Journal ArticleDOI
Phase retrieval techniques for radar ambiguity problems
TL;DR: In this paper, a partial answer for some classes of time limited (compactly supported) signals is given for the radar ambiguity problem, which is called the Bueckner ambiguity problem.
Related Papers (5)
Revisiting the Fourier transform on the Heisenberg group
Freiman theorem, fourier transform and additive structure of measures
Alex Iosevich,Misha Rudnev +1 more