2017/02/21 by Nicki Holighaus, Holighaus, Nicki, Péter Balázs +1
Computer Science · Earth and Planetary Sciences · Engineering · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Geophysics and Sensor Technology #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.1702.06485
openalex publication_date 2017/02/21 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
During the process of writing the manuscript ["Continuous warped\ntime-frequency representations - Coorbit spaces and discretization", N.\nHolighaus, C. Wiesmeyr and P. Balazs], the work ["Continuous Frames, Function\nSpaces and the Discretization Problem" by M. Fornasier and H. Rauhut - (1)] was\none of the major foundations of our results and, naturally, we found ourselves\ngoing back to reading that contribution once and again.\n In particular in Section 5, which is concerned with the discretization\nproblem, we have found some typographical errors, small inaccuracies and some\nparts that we just would have wished to be slightly more accessible. Finally,\nfor our own theory, a generalization of a central definition required us to\nverify that all the derivations in Section 5 of (1) still hold after the\nnecessary modifications.\n Considering the importance of the results in (1) for the community, this was\nreason enough to start this side project of re-writing that least accessible\nportion of Fornasier and Rauhut's manuscript, eliminating the errors we found,\nadding annotations where we consider them useful and modifying the results to\ntake into account the generalization we require for our own work.\n What you see is the result of our endeavor, a one-to-one substitute for\nSection 5 in (1).\n