Near-Parseval orbit frames for irreducible unitary representations: from mixing and expansion

[2608.15182] Near-Parseval orbit frames for irreducible unitary representations: from mixing and expansion Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Functional Analysis arXiv:2608.15182 (math) [Submitted on 15 Aug 2026] Title: Near-Parseval orbit frames for irreducible unitary representations: from mixing and expansion Authors: Vignon Oussa View a PDF of the paper titled Near-Parseval orbit frames for irreducible unitary representations: from mixing and expansion, by Vignon Oussa View PDF HTML (experimental) Abstract: We establish an abstract storage theorem for projectively $C_0$ unitary representations admitting a pair of one-parameter subgroups with conjugation escape. It produces, for every $0<\varepsilon<1$, a single orbit whose sampling set is relatively separated modulo the projective kernel and whose frame bounds are $(1-\varepsilon)^2$ and $(1+\varepsilon)^2$. Two applications are obtained from the same mechanism. First, every nonabelian exponential Lie group admits a near-Parseval frame of left translates for its left regular representation. Consequently, a positive-dimensional exponential Lie group is an FT group if and only if it is nonabelian; in particular, the three-dimensional Heisenberg group admits such a frame. Second, every infinite-dimensional irreducible unitary representation of an exponential Lie group admits a near-Parseval discrete orbit frame. When the effective projective quotient is abelian, the orbit may be chosen to be an orthonormal basis arising from a transported Weyl lattice. Comments: 36 pages, 4 figures. Appendix A documents the exact scope of a partial Lean 4/Mathlib certification; a Lean source archive is included as an ancillary file Subjects: Functional Analysis (math.FA) MSC classes: 22D10, 42C15 (Primary), 22E27, 22E46, 22E50, 43A65 (Secondary) Cite as: arXiv:2608.15182 [math.FA] (or arXiv:2608.15182v1 [math.FA] for this version) https://doi.org/10.48550/arXiv.2608.15182 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Vignon Oussa S [ view email ] [v1] Sat, 15 Aug 2026 11:46:51 UTC (64 KB) Full-text links: Access Paper: View a PDF of the paper titled Near-Parseval orbit frames for irreducible unitary representations: from mixing and expansion, by Vignon Oussa View PDF HTML (experimental) TeX Source view license Ancillary-file links: Ancillary files ( details ) : LeanCertificate/ARXIV_MAIN_SHA256.txt LeanCertificate/CERTIFICATION_SCOPE.md LeanCertificate/Core_Certificate_Lean_4_32_1/FramesSolvableRevisedCertificate.lean LeanCertificate/Core_Certificate_Lean_4_32_1/FramesSolvableRevisedCertificate/AlgebraicExamples.lean LeanCertificate/Core_Certificate_Lean_4_32_1/FramesSolvableRevisedCertificate/AxiomAudit.lean LeanCertificate/Core_Certificate_Lean_4_32_1/FramesSolvableRevisedCertificate/Main.lean LeanCertificate/Core_Certificate_Lean_4_32_1/FramesSolvableRevisedCertificate/Quantitative.lean LeanCertificate/Core_Certificate_Lean_4_32_1/FramesSolvableRevisedCertificate/RelativeSeparationCore.lean LeanCertificate/Core_Certificate_Lean_4_32_1/lake-manifest.json LeanCertificate/Core_Certificate_Lean_4_32_1/lakefile.lean LeanCertificate/Core_Certificate_Lean_4_32_1/lean-toolchain LeanCertificate/LICENSE_NOTE.txt LeanCertificate/Mathlib_Certificate_Lean_4_28_0/HeisenbergFrame/ArxivCertificate.lean LeanCertificate/Mathlib_Certificate_Lean_4_28_0/HeisenbergFrame/ArxivCertificateAxiomAudit.lean LeanCertificate/Mathlib_Certificate_Lean_4_28_0/HeisenbergFrame/Basic.lean LeanCertificate/Mathlib_Certificate_Lean_4_28_0/HeisenbergFrame/ColumnSynthesisWrapper.lean LeanCertificate/Mathlib_Certificate_Lean_4_28_0/HeisenbergFrame/DirectionalAffineEscape.lean LeanCertificate/Mathlib_Certificate_Lean_4_28_0/HeisenbergFrame/DirectionalAffineEscapeAxiomAudit.lean LeanCertificate/Mathlib_Certificate_Lean_4_28_0/HeisenbergFrame/PackingCore.lean LeanCertificate/Mathlib_Certificate_Lean_4_28_0/HeisenbergFrame/Perturbation.lean LeanCertificate/Mathlib_Certificate_Lean_4_28_0/HeisenbergFrame/RepeatedHilbertBasis.lean LeanCertificate/Mathlib_Certificate_Lean_4_28_0/HeisenbergFrame/RevisedAnalyticWrapper.lean LeanCertificate/Mathlib_Certificate_Lean_4_28_0/HeisenbergFrame/RevisedPreliminaries.lean LeanCertificate/Mathlib_Certificate_Lean_4_28_0/HeisenbergFrame/RevisedPreliminariesAxiomAudit.lean LeanCertificate/Mathlib_Certificate_Lean_4_28_0/HeisenbergFrame/ShearStageExtension.lean LeanCertificate/Mathlib_Certificate_Lean_4_28_0/lake-manifest.json LeanCertificate/Mathlib_Certificate_Lean_4_28_0/lakefile.toml LeanCertificate/Mathlib_Certificate_Lean_4_28_0/lean-toolchain LeanCertificate/README.md LeanCertificate/SOURCE_SHA256.txt LeanCertificate/verify.ps1 README.txt (27 additional files not shown) Current browse context: math.FA < prev | next > new | recent | 2026-08 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Near-Parseval orbit frames for irreducible unitary representations: from mixing and expansion#611128
• Towards a Quantum Erlangen Program#986940
• Generalised entanglement entropies from unit-invariant singular value decomposition#363679
• Unified spatiotemporal quantum states and spatiotemporal entanglement from Kirkwood-Dirac phase space#1051086
• Einstein's equation as a geometric encoding of correlations with quantum reference frames#793447