Gordon's conjectures 1 and 2: Pontryagin-van Kampen duality in the hyperfinite setting

DOI10.4115/jla.2021.13.1zbMath1486.22006arXiv1409.6128OpenAlexW3161477062WikidataQ123305921 ScholiaQ123305921MaRDI QIDQ4989720

Pavol Zlatoš

Publication date: 26 May 2021

Published in: Journal of Logic and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.6128

zbMATH Keywords

Fourier transformnonstandard analysislocally compact abelian groupPontryagin-van Kampen dualityhyperfiniteinfinitesimal approximation

Mathematics Subject Classification ID

Nonstandard models in mathematics (03H05) Locally compact groups and their algebras (22D99) Nonstandard measure theory (28E05) Nonstandard analysis (26E35) Nonstandard topology (54J05)

Related Items (1)

Gordon's Conjecture 3: Fourier transforms in the hyperfinite setting

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hilbert's fifth problem for local groups
• An elementary approach to Haar integration and Pontryagin duality in locally compact Abelian groups
• The syntax of nonstandard analysis
• Model theory.
• Nonstandard analysis and locally compact abelian groups
• Some Ramsey-type theorems for countably determined sets
• Foundations of time-frequency analysis
• The structure of approximate groups.
• Hyperfinite dimensional representations of spaces and algebras of measures
• Contribution to non-standard analysis
• The nonstandard hulls of a uniform space
• Approximate extension of partial \(\varepsilon\)-characters of Abelian groups to characters with application to integral point lattices.
• On approximation of topological groups by finite quasigroups and finite semigroups
• On approximation of unimodular groups by finite quasigroups
• Finite approximations to Lie groups
• Stable group theory and approximate subgroups
• Stability of group homomorphisms in the compact-open topology
• Nonstandard Measure Theory and its Applications
• Universal Loeb-Measurability of Sets and of the Standard Part Map with Applications
• Star-Finite Representations of Measure Spaces
• Conversion from Nonstandard to Standard Measure Spaces and Applications in Probability Theory
• Nonstandard hulls of locally uniform groups
• Freiman's theorem in an arbitrary abelian group
• How well does the finite Fourier transform approximate the Fourier transform?
• On approximations of groups, group actions, and Hopf algebras.

This page was built for publication: Gordon's conjectures 1 and 2: Pontryagin-van Kampen duality in the hyperfinite setting