250103 VO Frame Theory (2023W)
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Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).
Details
Language: English
Examination dates
Lecturers
Classes (iCal) - next class is marked with N
First meeting 03.10.2023 16:45
Tuesday
03.10.
16:45 - 18:15
Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
04.10.
16:45 - 17:30
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
10.10.
16:45 - 18:15
Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
11.10.
16:45 - 17:30
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
17.10.
16:45 - 18:15
Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
18.10.
16:45 - 17:30
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
24.10.
16:45 - 18:15
Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
25.10.
16:45 - 17:30
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
31.10.
16:45 - 18:15
Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday
07.11.
16:45 - 18:15
Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
08.11.
16:45 - 17:30
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
14.11.
16:45 - 18:15
Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
15.11.
16:45 - 17:30
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
21.11.
16:45 - 18:15
Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
22.11.
16:45 - 17:30
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
28.11.
16:45 - 18:15
Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
29.11.
16:45 - 17:30
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
05.12.
16:45 - 18:15
Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
06.12.
16:45 - 17:30
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
12.12.
16:45 - 18:15
Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
13.12.
16:45 - 17:30
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
09.01.
16:45 - 18:15
Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
10.01.
16:45 - 17:30
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
16.01.
16:45 - 18:15
Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
17.01.
16:45 - 17:30
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
23.01.
16:45 - 18:15
Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
24.01.
16:45 - 17:30
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
30.01.
16:45 - 18:15
Seminarraum 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
31.01.
16:45 - 17:30
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Information
Aims, contents and method of the course
Assessment and permitted materials
Written or oral exam.
Minimum requirements and assessment criteria
A basic understanding of concepts from functional analysis and linear algebra is expected for students to follow the course.For a successful conclusion of this course, students must demonstrate knowledge of the basic concepts and theorems, a basic understanding of the main proofs and applications presented, as well as a ability to use the techniques in similar results.
Examination topics
Everything that is covered in the course, and presented.The current plan is:
1.) Spanning sets in finite dimensional vector spaces
2.) Bessel sequences
3.) Riesz bases
4.) Frames
5.) Special topic in frame theory: e,g, phase retrieval, localization, ...
1.) Spanning sets in finite dimensional vector spaces
2.) Bessel sequences
3.) Riesz bases
4.) Frames
5.) Special topic in frame theory: e,g, phase retrieval, localization, ...
Reading list
The course will mostly stick to
Ole Christensen, An Introduction to Frames and Riesz Bases
Ole Christensen, An Introduction to Frames and Riesz Bases
Association in the course directory
MAMV; MANV
Last modified: We 13.03.2024 10:46
(i) recovered from its frame coefficients, i.e. the inner products with respect to the frame elements and
(ii) expanded into a linear combination of the frame elements.Frames have a rich structure despite being much less restrictive than ONBs, rendering them attractive for a wide number of applications. In addition to being an active field of research, posing interesting research questions of its own, frame theory has applications in other fields, like signal processing and physics.Students of this course will gain understanding of the basic properties of frames and Riesz bases in comparison to ONBs, both in a linear algebra and functional anaylsis context. The implementation of frame-related algorithms will be considered and applications in acoustics, signal processing, quantum mechanics and machine learning will be presented as motivation.For a short introduction see
https://en.wikipedia.org/wiki/Frame_(linear_algebra)This will be a standard frontal course, using mostly the blackboard and ocaasionally the beamer.