On discrete groups of Euclidean isometries: representation theory, harmonic analysis and splitting properties

DOI10.1007/s00041-023-10050-2arXiv2107.09571OpenAlexW3185243686MaRDI QIDQ6082546

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Publication date: 30 November 2023

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.09571

zbMATH Keywords

Fourier transformunitary representationsplittingdiscrete subgroupEuclidean group

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) (43A65) Other geometric groups, including crystallographic groups (20H15) Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. (43A30)

Cites Work

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• Existence and convergence of solutions of the boundary value problem in atomistic and continuum nonlinear elasticity theory
• Representation theory of finite groups. An introductory approach.
• Wavelets with crystal symmetry shifts
• Crystallographic Haar wavelets
• Unitary representations of group extensions. I
• Bieberbach groups and flat manifolds
• Separation of variables and the computation of Fourier transforms on finite groups. II
• The efficient computation of Fourier transforms on semisimple algebras
• Duals of crystallographic groups. Band and quasi-band representations
• Objective structures
• Induced representation of locally compact groups. I
• Decomposing the wavelet representation for shifts by wallpaper groups
• On the stability of Bravais lattices and their Cauchy–Born approximations
• Induced Representations of Locally Compact Groups
• Geometry of Crystallographic Groups
• Foundations of Hyperbolic Manifolds
• On Induced Representations of Discrete Groups
• Comments on the decomposition of the regular representation of crystallographic space groups into band representations
• A Bieberbach Theorem for crystallographic group extensions
• Toward a Mathematical Theory of the Crystallographic Phase Retrieval Problem
• The crystallographic fast Fourier transform. Recursive symmetry reduction
• Symmetry and Condensed Matter Physics
• Groups with Finite Dimensional Irreducible Representations
• The plancherel formula for group extensions
• The plancherel formula for group extensions II
• Separation of variables and the computation of Fourier transforms on finite groups, I
• On Induced Representations of Groups

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