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We revisit the concept of samplets, a multiresolution analysis of discrete signed measures with prescribed vanishing moments. Samplets enable efficient data compression, feature detection and adaptive representations. The decay of samplet coefficients can be employed to quantify pointwise regularity within the framework of microlocal spaces introduced
by Jaffard.
Within the framework of reproducing kernel Hilbert spaces, samplets induce specific bases in subspaces spanned by kernel translates via the Riesz isometry. The corresponding Gramian, that is, the kernel matrix expressed in samplet coordinates, becomes quasi-sparse for quasiuniform data sites. The compression error is controllable by the number of vanishing moments when considering asymptotically smooth kernels. Furthermore, the compressed representation can be computed efficiently by leveraging H2-matrix techniques. We present the corresponding algorithms in detail and report favorable numerical results.

The guest talk will take place on November 11, 2025 from 4:30 - 5:30 pm in S 88 (BGI).