Gabor bases and frames

Seminar Schedule — November

Links, abstracts, and milestones
Updated

Date Week / Meeting Topic & Abstract
Week 1 — Meeting 1
Abstract
We work in \(L^2(\mathbb{R})\) with its inner product and induced 2-norm.
We introduce two fundamental unitary operators—translation and modulation—
parametrized by \(\mathbb{R}^2\). The group they generate is the non-commutative,
three-parameter Heisenberg group, whose action on \(L^2(\mathbb{R})\)
is central in time–frequency analysis and supports constructions of
orthonormal bases and frames.
Week 1 — Meeting 2
Homework Submit on Gradescope
Veterans Day — no class
No Class
Week 2 — Meeting 1
Week 2 Topic: Preparing for the final paper
Guidelines
Select two assigned homework problems and synthesize them into a ~15-page
mathematical article (title, abstract, introduction with context, one main theorem
supported by propositions/lemmas). Write in the customary style of mathematical
exposition. An example article is provided separately.
Week 2 — Meeting 2 Gabor basis with a continuous window
Week 3 — Meeting 1 Draft due:
Article skeleton (title, abstract, tentative main result).
Milestone
Week 3 — Meeting 2
Thanksgiving Recess — no class
No Class