Stockwell-like frames for Sobolev spaces

Abstract

We construct a family of frames describing Sobolev norm and Sobolev seminorm of the space H s (R n ). 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. 1 arXiv:1605.08691v1 [math.FA]