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Record W4412299086

Knapp-Stein Operators and Fourier Transformations

2019· article· da· W4412299086 on OpenAlexaff
Tue Thulesen Dahl

Bibliographic record

Venuenot available
Typearticle
Languageda
FieldMathematics
Topicadvanced mathematical theories
Canadian institutionsToronto Metropolitan University
Fundersnot available
KeywordsFourier transformMathematicsArtMathematical analysis
DOInot available

Abstract

fetched live from OpenAlex

I afhandlingen analyserer vi visse Knapp-Stein sammenfletningsoperator via distributionsteori på Liegrupper. Sådan en operator virker ved foldning med en distribution i enten det kompakte eller det ikkekompakte billede og vi undersøger om distributionen er positivt definit. I bekræftende fald kan operatoren bruges til at konstruere nye invariante indre produkter og dermed nye repræsentationer.<br/><br/>På en vilkårlig kompakt Liegruppe K giver vi en Bochners Sætning, der bestemmer hvornår en distribution (med operatorværdier) er positivt defninit. På Heisenberggruppen N konstruerer vi en Fouriertransformation, der bestemmer hvornår en distribution er positivt definit på et bestemt *-ideal i algebraen af Schwartzfunktioner på N. Konstruktionen bruger teorien om tensorprodukter af topologiske vektorrum: Givet to hypokontinuerte bilineære afbildninger har vi brug for at vide, at deres ``tensor produktet'' er hypokontinuert. Vi beviser sådan en sætning i tilfældet hvor nogle af de involverede rum er af type F eller DF.<br/><br/>Til sidst udregner vi Knapp-Stein-kernerne og analyserer deres Fouriertransformation i tre tilfælde: Først betragter vi SL(d, R) med en stor parabolsk undergruppe ``i midten'' og repræsentationer induceret fra karaktererne i N-billedet. Dernæst betrager vi den samme repræsentation i tilfældet d = 3 på K, og til sidst betragter vi den dobbelte overdækning af SL(3, R) i det kompakte billede, hvor K = SU(2), og vi inducerer fra den karakteristiske repræsentation af M som undergruppe af SU(2). For et bestemt valg af parametrer giver dette en ny og eksplicit konstruktion af Torassorepræsentationen.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Insufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.334
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.001
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0060.003

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.016
GPT teacher head0.283
Teacher spread0.267 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; both teacher heads agree on what is shown here.

Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".

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Citations1
Published2019
Admission routes1
Has abstractyes

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