Abstract
Let π : G → U(X) be an irreducible and square-integrable representation of a locally compact and Hausdorff group G on a Hilbert space X. Then for all functions F in L p (G), 1 ≤ p ≤ ∞, and all admissible wavelets φ for π : G → U(X), Proposition 12.3 ensures that we can get a unique bounded linear operator L F,φ : X → X such that
and
for all x and y in X whenever F is a simple function on G for which
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© 2002 Springer Basel AG
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Wong, M.W. (2002). Hilbert-Schmidt Localization Operators. In: Wavelet Transforms and Localization Operators. Operator Theory: Advances and Applications, vol 136. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8217-0_15
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DOI: https://doi.org/10.1007/978-3-0348-8217-0_15
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9478-4
Online ISBN: 978-3-0348-8217-0
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