The quaternionic affine group and related continuous wavelet transforms on complex and quaternionic Hilbert spaces

DOI10.1063/1.4881716zbMath1305.42035arXiv1402.3109OpenAlexW2962806527MaRDI QIDQ5171414

K. Thirulogasanthar, Syed Twareque Ali

Publication date: 26 July 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.3109

zbMATH Keywords

quaternionic Hilbert spacequaternionic affine groupquaternionic wavelets

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Unitary representations of locally compact groups (22D10) Linear algebraic groups over the reals, the complexes, the quaternions (20G20)

Related Items (6)

Discretization of quaternionic continuous wavelet transforms ⋮ A variation on uncertainty principle and logarithmic uncertainty principle for continuous quaternion wavelet transforms ⋮ General double-sided orthogonal planes split QFT and wavelet transform on functions and distribution spaces ⋮ Uncertainty principles related to quaternionic windowed Fourier transform ⋮ Discrete frames for \(L^2(\mathbb{R}^{n^2})\) arising from tiling systems on \(\mathrm{GL}_n(\mathbb{R})\) ⋮ Quaternionic continuous wavelet transform on a quaternionic Hilbert space

Cites Work

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• CONTINUOUS SLICE FUNCTIONAL CALCULUS IN QUATERNIONIC HILBERT SPACES
• A four dimensional continuous wavelet transform
• Ten Lectures on Wavelets
• Normal Operators on Quaternionic Hilbert Spaces
• Quaternions and matrices of quaternions

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