Group representations in reproducing kernel Hilbert spaces

DOI10.1016/0034-4877(78)90047-2zbMath0418.22004OpenAlexW2061875984MaRDI QIDQ755689

Alan L. Carey

Publication date: 1978

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0034-4877(78)90047-2

zbMATH Keywords

group representationslocally compact groupreproducing kernel Hilbert spacepositive definite functionconvolution construction

Mathematics Subject Classification ID

Unitary representations of locally compact groups (22D10) Positive definite functions on groups, semigroups, etc. (43A35)

Related Items (14)

Reproducing kernel Hilbert spaces and extremal problems for scattering of particles with arbitrary spins ⋮ Admissible vectors for the regular representation ⋮ Holomorphic and abstract inducing ⋮ Homogeneous vector bundles and \(G\)-equivariant convolutional neural networks ⋮ Quantization of a classical system on a coadjoint orbit of the Poincaré group in 1+1 dimensions ⋮ Irreducibility of unitary group representations and reproducing kernels Hilbert spaces. Appendix on two point homogeneous compact ultrametric spaces in collaboration with Rostislav Grigorchuk. ⋮ Admissible vectors and Hilbert algebras ⋮ Square-integrable representations of non-unimodular groups ⋮ A wavelet transform for the Poincaré group ⋮ Sound and symmetry ⋮ Scaling and s-channel helicity conservation via optimal state description of hadron-hadron scattering ⋮ Unnamed Item ⋮ EXTENDED WAVELET TRANSFORMS ⋮ Reproducing kernel Hilbert spaces and optimal state description of hadron-hadron scattering

Cites Work

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• Coherent states for arbitrary Lie group
• Representations of Semisimple Lie Groups VI: Integrable and Square-Integrable Representations
• Functional Analysis and Related Fields
• The Dimension of Spaces of Automorphic Forms
• Les Fonctions De Type Positif et la Theorie Des Groupes
• Theory of Reproducing Kernels
• SOME PROPERTIES OF EIGENFUNCTION EXPANSIONS
• An extension of Plancherel's formula to separable unimodular groups

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