Translation-invariant integrals, and Fourier analysis on Clifford and Grassmann algebras

DOI10.1016/0022-1236(80)90028-2zbMath0434.43007OpenAlexW2091679926MaRDI QIDQ1139768

S. N. Peck, Robin L. Hudson, Mark D. Wilkinson

Publication date: 1980

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(80)90028-2

zbMATH Keywords

central limit theoremClifford algebratwisted convolutionFourier-Weyl transformationtranslation invariant integral

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Clifford algebras, spinors (15A66) Other transforms and operators of Fourier type (43A32) Duality theorems for locally compact groups (22D35) Exterior algebra, Grassmann algebras (15A75)

Related Items (7)

Infinitely divisible completely positive mappings ⋮ Graph-theoretic approach to stochastic integrals with Clifford algebras ⋮ Convergence for noncommutative rational functions evaluated in random matrices ⋮ A non-commutative central limit theorem ⋮ A noncommutative central limit theorem for CCR-algebras ⋮ The Clifford algebra of differential forms ⋮ The strong Markov property for fermion Brownian motion

Cites Work

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• On the formula of Mathews and Salam
• Translation-invariant traces and Fourier analysis on multiplier representation of vector groups
• The free fermion field as a Markov field
• States of the Clifford algebra
• Existence and uniqueness of physical ground states
• A non-commutative extension of abstract integration
• An algebraic central limit theorem in the anti-commuting case
• Transforms for Operators and Symplectic Automorphisms over a Locally Compact Abelian Group.
• Infinitely divisible representations of Clifford algebras
• A quantum-mechanical central limit theorem

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