Seminar Schedule — November
Links, abstracts, and milestones
Updated
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 | ||
| — |
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 |
Week 3 Topic:
Construction of Gabor frames with non integer lattices |
|
| — |
Thanksgiving Recess — no class No Class |