Gordon's Conjecture 3: Fourier transforms in the hyperfinite setting
DOI10.4115/jla.2021.13.7zbMath1492.43004OpenAlexW4210704418WikidataQ113692094 ScholiaQ113692094MaRDI QIDQ5028383
Publication date: 9 February 2022
Published in: Journal of Logic and Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.4115/jla.2021.13.7
Fourier transformapproximationnonstandard analysisinfinitesimallocally compact abelian groupPontryagin-van Kampen dualityhyperfinite
(L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15) Nonstandard functional analysis (46S20) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25) Nonstandard measure theory (28E05) Measure algebras on groups, semigroups, etc. (43A10) Nonstandard analysis (26E35) (L^1)-algebras on groups, semigroups, etc. (43A20)
Cites Work
- Nonstandard analysis - recent developments
- On Kolmogorov-Tamarkin and M. Riesz compactness criteria in function spaces over a locally compact group
- Nonstandard analysis and locally compact abelian groups
- Foundations of time-frequency analysis
- Hyperfinite dimensional representations of spaces and algebras of measures
- Measure algebras on abelian groups
- Compactness in L 2 and the Fourier Transform
- Gordon's conjectures 1 and 2: Pontryagin-van Kampen duality in the hyperfinite setting
- How well does the finite Fourier transform approximate the Fourier transform?
- Finite-dimensional approximations of operators in the Hilbert spaces of functions on locally compact Abelian groups
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