Abstract Harmonic Analysis of Continuous Wavelet Transforms

By Hartmut Fuhr. 2005

318 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6be25f66e4d836982b9c6f43f28d232e100d4a99

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Vector valued reproducing kernel Hilbert spaces and universality (2008, background): “This operator is well know in harmonic analysis as wavelet operator [17].”
Continuous Wavelets and Frames on Stratified Lie Groups I (2006, background): “…C1c , then for x outside the support of f , (Tf)(x) = ∫ K(x, y)f(y)dy; and whenever 0 ≤ α1 + . . . + αn + β1 + . . . + βn ≤ 1, and whenever x, y ∈ G with x 6= y, we have |XαxXβyK(x, y)| ≤ A0|y−1x|−Q−|α|−|β|; and (72) (iii) T ∗(1) = 0; then T |L2∩B extends to a bounded operator on B, with norm ‖T…”
VECTOR VALUED REPRODUCING KERNEL HILBERT SPACES OF INTEGRABLE FUNCTIONS AND MERCER THEOREM (2006, background): “The problem of square-integrability is discussed in the framework of harmonic analysis in connection with square-integrable representations (there is a large literature on the topic, see for example [5, 6] and references therein); in a general setting there are some sufficient conditions in [4].”
Sampling theorems on locally compact groups from oscillation estimates (2005, unknown): “[21] and the references therein for details.”
Coorbit spaces and wavelet coefficient decay over general dilation groups (2012, background): “Moreover, recent investigations of wavelet inversion formulae (such as [20,22,27]) and of coorbit theory [3–5] beyond the irreducible setting indicate that irreducibility may not be essential for the development of coorbit space theory.”
Sampling in paley-wiener spaces on combinatorial graphs (2008, methodology): “Some of the ideas and methods of this theory were recently extended to the cases of Riemannian manifolds, symmetric spaces, groups, and quantum graphs [7], [8], [10], [11], [14], [15], [25]-[32].”