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Found 4 Results
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Energy and Discrepancy on Hamming Spaces

In 1973, Stolarsky discovered a connection between the quadratic spherical cap discrepancy of a point set on the sphere, and it's sum of Euclidean distances between pairs of distinct points, showing that minimizing the discrepancy was equivalent to maximizing the sum of distances. In this talk, we discuss an analogue of this result for the Hamming [Read More...]

Presenter: Ryan W Matzke, Vanderbilt University
Symposium Year: 2023
Session: Special Session on Discrete Harmonic Analysis [Organized by Christina Giannitsi and Michael Lacey]
Presentation Time: September 30, 2023; 9:45 am

Discrete non-linear Fourier transform via spectral problems for canonical systems

This talk will be about the connections between discrete non-linear Fourier transforms (NLFTs) and Dirac systems. Non-linear Fourier transform is known to be closely related to Dirac systems, which form a subclass of canonical systems of differential equations. This connection allows one to find analogs of results on spectral problems in the area of NLFT. [Read More...]

Presenter: Ashley Zhang, Vanderbilt University
Symposium Year: 2023
Session: Special Session on Discrete Harmonic Analysis [Organized by Christina Giannitsi and Michael Lacey]
Presentation Time: September 30, 2023; 10:10 am

Compactness of the Bloom sparse operators and applications

We discuss the characterization of compactness for the sparse operator (associated with symbol in weighted VMO space) in the two-weight setting on the spaces of homogeneous type. As a direct application we obtain the compactness characterization for the maximal commutators with respect to the weighted VMO functions and the commutator of Calderon–Zygmund [Read More...]

Presenter: Naga Manasa Vempati, Louisiana State University
Authors: Peng Chen, Michael Lacey, Ji Li, Manasa N. Vempati
Symposium Year: 2023
Session: Special Session on Discrete Harmonic Analysis [Organized by Christina Giannitsi and Michael Lacey]
Presentation Time: September 30, 2023; 10:35 am

Recent results on averages along prime numbers

We will survey some recent results about averages over primes, both in the integers, and in a number field setting. The questions concern improving properties of averages formed over prime numbers. The methods of proof also address questions related to representations of integers as sums of primes, including some generalizations of the Vinogradov Three [Read More...]

Presenter: Michael Lacey, Georgia Tech
Authors: Christina Giannitsi, Ben Krause, Hamed Mousavi, Yaghoub Rahimi,
Symposium Year: 2023
Session: Special Session on Discrete Harmonic Analysis [Organized by Christina Giannitsi and Michael Lacey]
Presentation Time: September 30, 2023; 11:00 am
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