NDLI: Tight frames generated by finite nonabelian groups

Content Provider	Springer Nature Link
Author	Waldron, Shayne Vale, Richard
Copyright Year	2008
Abstract	Let $\cal H$ be a Hilbert space of finite dimension d, such as the finite signals ℓ $_{2}$(d) or a space of multivariate orthogonal polynomials, and n ≥ d. There is a finite number of tight frames of n vectors for $\cal H$ which can be obtained as the orbit of a single vector under the unitary action of an abelian group G (of symmetries of the frame). Each of these so called harmonic frames or geometrically uniform frames can be obtained from the character table of G in a simple way. These frames are used in signal processing and information theory. For a nonabelian group G there are in general uncountably many inequivalent tight frames of n vectors for $\cal H$ which can be obtained as such a G-orbit. However, by adding an additional natural symmetry condition (which automatically holds if G is abelian), we obtain a finite class of such frames which can be constructed from the character table of G in a similar fashion to the harmonic frames. This is done by identifying each G-orbit with an element of the group algebra ℂG (via its Gramian), imposing the condition in the group algebra, and then describing the corresponding class of tight frames.
Ending Page	27
Page Count	17
Starting Page	11
File Format	PDF
ISSN	10171398
e-ISSN	15729265
Journal	Numerical Algorithms
Issue Number	1-3
Volume Number	48
Language	English
Publisher	Springer US
Publisher Date	2008-03-18
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Geometrically uniform frames Ordinary representations and characters Group matrices Signal theory (characterization, reconstruction, filtering, etc.) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) Numeric Computing Theory of Computation Mathematics Tight frames Gramian matrix Application of orthogonal and other special functions Multidimensional problems (should also be assigned at least one other classification number in this section) Wavelets Algebra Algorithms Signal processing Representation theory Harmonic frames General harmonic expansions, frames Central tight G-frames Information theory, general Information theory Finite nonabelian groups
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Dual fusion frames

Dual Fusion Frames

Optimal Non-Linear Models for Sparsity and Sampling

Recovering functions from the Paley-Wiener amalgam space

Kaczmarz algorithm in Hilbert space and tight frames

Frames and weak frames for unbounded operators

Native spaces and generalization of Wu functions

Continuous frames for unbounded operators

Irregular Shearlet Frames: Geometry and Approximation Properties

Tight frames generated by finite nonabelian groups

Similar Documents

Dual fusion frames

Dual Fusion Frames

Optimal Non-Linear Models for Sparsity and Sampling

Recovering functions from the Paley-Wiener amalgam space

Kaczmarz algorithm in Hilbert space and tight frames

Frames and weak frames for unbounded operators

Native spaces and generalization of Wu functions

Continuous frames for unbounded operators

Irregular Shearlet Frames: Geometry and Approximation Properties

Tight frames generated by finite nonabelian groups