Displaying similar documents to “Boundedness of the wavelet transform in certain function spaces.”

A gradient-projective basis of compactly supported wavelets in dimension n > 1

Guy Battle (2013)

Open Mathematics

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A given set W = W X of n-variable class C 1 functions is a gradient-projective basis if for every tempered distribution f whose gradient is square-integrable, the sum ∑ χ ( ∫ ℝ n ∇ f · ∇ W χ * ) W χ converges to f with respect to the norm ∇ ( · ) L 2 ( ℝ n ) . The set is not necessarily an orthonormal set; the orthonormal expansion formula is just an element of the convex set of valid expansions of the given function f over W. We construct a gradient-projective basis W = W x of compactly supported class C 2−ɛ functions on ℝn such...

An extension of distributional wavelet transform

R. Roopkumar (2009)

Colloquium Mathematicae

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We construct a new Boehmian space containing the space 𝓢̃'(ℝⁿ×ℝ₊) and define the extended wavelet transform 𝓦 of a new Boehmian as a tempered Boehmian. In analogy to the distributional wavelet transform, it is proved that the extended wavelet transform is linear, one-to-one, and continuous with respect to δ-convergence as well as Δ-convergence.

Wavelet transform for functions with values in UMD spaces

Cornelia Kaiser, Lutz Weis (2008)

Studia Mathematica

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We extend the classical theory of the continuous and discrete wavelet transform to functions with values in UMD spaces. As a by-product we obtain equivalent norms on Bochner spaces in terms of g-functions.