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arXiv · 1605.08691

Stockwell-Like Frames for Sobolev Spaces

Ubertino Battisti·Michele Berra·Anita Tabacco
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Abstract

We construct a family of frames describing Sobolev norm and Sobolev seminorm of the space $H^s(\mathbb{R}^d)$. Our work is inspired by the Discrete Orthonormal Stockwell Transform introduced by R.G. Stockwell, which provides a time-frequency localized version of Fourier basis of $L^2([0,1])$. This approach is a hybrid between Gabor and Wavelet frames. We construct explicit and computable examples of these frames, discussing their properties.

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Ubertino Battisti, Michele Berra, Anita Tabacco. 2016-05-27. Stockwell-Like Frames for Sobolev Spaces. https://arxiv.org/abs/1605.08691

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