3 years ago

Stockwell-like frames for Sobolev spaces

Michele Berra, Ubertino Battisti, Anita Tabacco


We construct a family of frames describing the norm and seminorm of the space \(H^s(\mathbb {R}^d)\) . We also characterise Besov spaces modeled on \(L^2(\mathbb {R}^d)\) . Our work is inspired by the discrete orthonormal Stockwell transform introduced by R.G. Stockwell, which provides a time-frequency localised version of the 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 and comparing them with the existing literature.

Publisher URL: https://link.springer.com/article/10.1007/s11868-018-0259-7

DOI: 10.1007/s11868-018-0259-7

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