Advanced search options

Advanced Search Options 🞨

Browse by author name (“Author name starts with…”).

Find ETDs with:

in
/  
in
/  
in
/  
in

Written in Published in Earliest date Latest date

Sorted by

Results per page:

Sorted by: relevance · author · university · dateNew search

You searched for subject:(LCA group). Showing records 1 – 2 of 2 total matches.

Search Limiters

Last 2 Years | English Only

No search limiters apply to these results.

▼ Search Limiters


University of Oregon

1. Iverson, Joseph. Frames Generated by Actions of Locally Compact Groups.

Degree: PhD, Department of Mathematics, 2016, University of Oregon

Let G be a second countable, locally compact group which is either compact or abelian, and let ρ be a unitary representation of G on a separable Hilbert space \mathcal{H}_ρ. We examine frames of the form { ρ(x) fj \colon x ∈ G, j ∈ I} for families {fj}j ∈ I in \mathcal{H}_ρ. In particular, we give necessary and sufficient conditions for the joint orbit of a family of vectors in \mathcal{H}_ρ to form a continuous frame. We pay special attention to this problem in the setting of shift invariance. In other words, we fix a larger second countable locally compact group Γ \supset G containing G as a closed subgroup, and we let ρ be the action of G on L2(Γ) by left translation. In both the compact and the abelian settings, we introduce notions of Zak transforms on L2(Γ) which simplify the analysis of group frames. Meanwhile, we run a parallel program that uses the Zak transform to classify closed subspaces of L2(Γ) which are invariant under left translation by G. The two projects give compatible outcomes. This dissertation contains previously published material. Advisors/Committee Members: Bownik, Marcin (advisor).

Subjects/Keywords: Compact group; Dual integrable; Group frame; LCA group; Shift-invariant; Zak transform

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Iverson, J. (2016). Frames Generated by Actions of Locally Compact Groups. (Doctoral Dissertation). University of Oregon. Retrieved from http://hdl.handle.net/1794/20443

Chicago Manual of Style (16th Edition):

Iverson, Joseph. “Frames Generated by Actions of Locally Compact Groups.” 2016. Doctoral Dissertation, University of Oregon. Accessed September 19, 2020. http://hdl.handle.net/1794/20443.

MLA Handbook (7th Edition):

Iverson, Joseph. “Frames Generated by Actions of Locally Compact Groups.” 2016. Web. 19 Sep 2020.

Vancouver:

Iverson J. Frames Generated by Actions of Locally Compact Groups. [Internet] [Doctoral dissertation]. University of Oregon; 2016. [cited 2020 Sep 19]. Available from: http://hdl.handle.net/1794/20443.

Council of Science Editors:

Iverson J. Frames Generated by Actions of Locally Compact Groups. [Doctoral Dissertation]. University of Oregon; 2016. Available from: http://hdl.handle.net/1794/20443


University of North Texas

2. Cotton, Michael R. Abelian Group Actions and Hypersmooth Equivalence Relations.

Degree: 2019, University of North Texas

We show that any Borel action on a standard Borel space of a group which is topologically isomorphic to the sum of a countable abelian group with a countable sum of lines and circles induces an orbit equivalence relation which is hypersmooth. We also show that any Borel action of a second countable locally compact abelian group on a standard Borel space induces an orbit equivalence relation which is essentially hyperfinite, generalizing a result of Gao and Jackson for the countable abelian groups. Advisors/Committee Members: Gao, Su, Jackson, Stephen C., Kallman, Robert R..

Subjects/Keywords: abelian; group action; hypersmooth; equivalence relation; Borel; hyperfinite; essentially hyperfinite; locally compact; LCA-group

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Cotton, M. R. (2019). Abelian Group Actions and Hypersmooth Equivalence Relations. (Thesis). University of North Texas. Retrieved from https://digital.library.unt.edu/ark:/67531/metadc1505289/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Cotton, Michael R. “Abelian Group Actions and Hypersmooth Equivalence Relations.” 2019. Thesis, University of North Texas. Accessed September 19, 2020. https://digital.library.unt.edu/ark:/67531/metadc1505289/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Cotton, Michael R. “Abelian Group Actions and Hypersmooth Equivalence Relations.” 2019. Web. 19 Sep 2020.

Vancouver:

Cotton MR. Abelian Group Actions and Hypersmooth Equivalence Relations. [Internet] [Thesis]. University of North Texas; 2019. [cited 2020 Sep 19]. Available from: https://digital.library.unt.edu/ark:/67531/metadc1505289/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Cotton MR. Abelian Group Actions and Hypersmooth Equivalence Relations. [Thesis]. University of North Texas; 2019. Available from: https://digital.library.unt.edu/ark:/67531/metadc1505289/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

.