Universität Wien FIND
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250047 VO Frame Theory (2019W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

An/Abmeldung

Details

Sprache: Englisch

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

Montag 07.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Donnerstag 10.10. 16:45 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Montag 14.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Donnerstag 17.10. 16:45 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Montag 21.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Donnerstag 24.10. 16:45 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Montag 28.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Donnerstag 31.10. 16:45 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Montag 04.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Donnerstag 07.11. 16:45 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Montag 11.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Donnerstag 14.11. 16:45 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Montag 18.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Donnerstag 21.11. 16:45 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Montag 25.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Donnerstag 28.11. 16:45 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Montag 02.12. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Donnerstag 05.12. 16:45 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Montag 09.12. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Donnerstag 12.12. 16:45 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Montag 16.12. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Donnerstag 09.01. 16:45 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Montag 13.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Donnerstag 16.01. 16:45 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Montag 20.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Donnerstag 23.01. 16:45 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Montag 27.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Donnerstag 30.01. 16:45 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

Frame theory is concerned with the study of stable, potentially overcomplete spanning sets in a Hilbert space. Its starting point is a generalization of the principle of an orthonormal basis resulting in the definition of a frame. Similar to orthonormal bases (ONBs) every function can be
(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. Particular The implementation of frame-related algorithms will be considered and applications in acoustics, signal processing and quantum mechanics are 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.

Art der Leistungskontrolle und erlaubte Hilfsmittel

Written exam

(In exceptional cases an oral exam is possible.)

Mindestanforderungen und Beurteilungsmaßstab

A basic understanding of concepts from functional analysis and linear algebra.

For a successful conclusion of this course, students must demonstrate knowledge of the basic concepts and theorems, as well as an understanding of the main proofs and applications presented.

Prüfungsstoff

Everything that is covered in the course, i.e.
1.) Spanning sets in finite dimensional vector spaces
2.) Bessel sequences
3.) Riesz bases
4.) Frames
5.) Particular frame systems: Gabor, Wavelets, Shift-invariant Systems

Literatur

The course will mostly stick to
Ole Christensen, An Introduction to Frames and Riesz Bases

Zuordnung im Vorlesungsverzeichnis

MANV, MAMV

Letzte Änderung: Mi 28.08.2019 12:48