NDLI: Different Faces of the Shearlet Group

Content Provider	Springer Nature Link
Author	Dahlke, Stephan De Mari, Filippo De Vito, Ernesto Häuser, Sören Steidl, Gabriele Teschke, Gerd
Copyright Year	2015
Abstract	Recently, shearlet groups have received much attention in connection with shearlet transforms applied for orientation sensitive image analysis and restoration. The square integrable representations of the shearlet groups provide not only the basis for the shearlet transforms but also for a very natural definition of scales of smoothness spaces, called shearlet coorbit spaces. The aim of this paper is twofold: first we discover isomorphisms between shearlet groups and other well-known groups, namely extended Heisenberg groups and subgroups of the symplectic group. Interestingly, the connected shearlet group with positive dilations has an isomorphic copy in the symplectic group, while this is not true for the full shearlet group with all nonzero dilations. Indeed we prove the general result that there exist, up to adjoint action of the symplectic group, only one embedding of the extended Heisenberg algebra into the Lie algebra of the symplectic group. Having understood the various group isomorphisms it is natural to ask for the relations between coorbit spaces of isomorphic groups with equivalent representations. These connections are examined in the second part of the paper. We describe how isomorphic groups with equivalent representations lead to isomorphic coorbit spaces. In particular we apply this result to square integrable representations of the connected shearlet groups and metaplectic representations of subgroups of the symplectic group. This implies the definition of metaplectic coorbit spaces. Besides the usual full and connected shearlet groups we also deal with Toeplitz shearlet groups.
Starting Page	1693
Ending Page	1729
Page Count	37
File Format	PDF
ISSN	10506926
Journal	Journal of Geometric Analysis
Volume Number	26
Issue Number	3
e-ISSN	1559002X
Language	English
Publisher	Springer US
Publisher Date	2015-04-11
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Shearlet group Heisenberg group Symplectic group Coorbit space theory Unitary representations of locally compact groups Analysis on real and complex Lie groups Lie algebras of Lie groups Function spaces arising in harmonic analysis General harmonic expansions, frames Differential Geometry Convex and Discrete Geometry Fourier Analysis Abstract Harmonic Analysis Dynamical Systems and Ergodic Theory Global Analysis and Analysis on Manifolds
Content Type	Text
Resource Type	Article
Subject	Geometry and Topology

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

Different faces of the shearlet group

Shearlet coorbit spaces: traces and embeddings in higher dimensions

The Continuous Shearlet Transform in Arbitrary Space Dimensions

Shearlet Coorbit Spaces: Compactly Supported Analyzing Shearlets, Traces and Embeddings

Moment convexity of solvable locally compact groups

On automorphism groups acting ergodically on connected locally compact groups, ergodic theory and harmonic analysis (1999).

Coorbit Spaces with Voice in a Fréchet Space

Explicit Ricci Solitons on Nilpotent Lie Groups

Compact Heisenberg manifolds as CR manifolds

Different Faces of the Shearlet Group

Similar Documents

Different faces of the shearlet group

Shearlet coorbit spaces: traces and embeddings in higher dimensions

The Continuous Shearlet Transform in Arbitrary Space Dimensions

Shearlet Coorbit Spaces: Compactly Supported Analyzing Shearlets, Traces and Embeddings

Moment convexity of solvable locally compact groups

On automorphism groups acting ergodically on connected locally compact groups, ergodic theory and harmonic analysis (1999).

Coorbit Spaces with Voice in a Fréchet Space

Explicit Ricci Solitons on Nilpotent Lie Groups

Compact Heisenberg manifolds as CR manifolds

Different Faces of the Shearlet Group