@article{MR4383342,
author = {Nielsen, Morten},
date-added = {2023-01-27 10:19:12 +0100},
date-modified = {2023-01-27 10:19:12 +0100},
doi = {10.1007/s00009-022-02001-w},
fjournal = {Mediterranean Journal of Mathematics},
issn = {1660-5446},
journal = {Mediterr. J. Math.},
mrclass = {42B35 (42C15 42C40)},
mrnumber = {4383342},
number = {2},
pages = {Paper No. 55, 18},
title = {Unconditional bases for homogeneous {$\alpha$}-modulation type spaces},
url = {https://doi.org/10.1007/s00009-022-02001-w},
volume = {19},
year = {2022},
bdsk-url-1 = {https://doi.org/10.1007/s00009-022-02001-w}
}
@article{MR4376564,
author = {Gribonval, R\'{e}mi and Kutyniok, Gitta and Nielsen, Morten and Voigtlaender, Felix},
date-added = {2023-01-27 10:19:12 +0100},
date-modified = {2023-01-27 10:19:12 +0100},
doi = {10.1007/s00365-021-09543-4},
fjournal = {Constructive Approximation. An International Journal for Approximations and Expansions},
issn = {0176-4276},
journal = {Constr. Approx.},
mrclass = {41A46 (41A63 42C40 65D15 68T07)},
mrnumber = {4376564},
number = {1},
pages = {259--367},
title = {Approximation spaces of deep neural networks},
url = {https://doi.org/10.1007/s00365-021-09543-4},
volume = {55},
year = {2022},
bdsk-url-1 = {https://doi.org/10.1007/s00365-021-09543-4}
}
@article{MR3707993,
author = {Cleanthous, G. and Georgiadis, A. G. and Nielsen, M.},
date-added = {2021-09-20 08:38:29 +0200},
date-modified = {2021-09-20 08:38:29 +0200},
doi = {10.1007/s12220-017-9781-8},
fjournal = {Journal of Geometric Analysis},
issn = {1050-6926},
journal = {J. Geom. Anal.},
mrclass = {42B25 (42B30 42B35 46F10)},
mrnumber = {3707993},
mrreviewer = {Charles N. Moore},
number = {4},
pages = {2758--2787},
title = {Anisotropic mixed-norm {H}ardy spaces},
url = {https://doi-org.zorac.aub.aau.dk/10.1007/s12220-017-9781-8},
volume = {27},
year = {2017},
bdsk-url-1 = {https://doi-org.zorac.aub.aau.dk/10.1007/s12220-017-9781-8},
bdsk-url-2 = {https://doi.org/10.1007/s12220-017-9781-8}
}
@article{458b9d984f0440a7afb3108bbfa1ec11,
abstract = {In this paper we derive an orthonormal basis of wavelet scaling functions for L2 ([0, 1]) motivated by the need for such a basis in the field of generalized sampling. A special property of this basis is that it includes carefully constructed boundary functions and it can be constructed with arbitrary smoothness. This construction makes assumptions about the signal outside the interval unnecessary. Furthermore, we provide a Python package implementing this wavelet decomposition. Wavelets defined on a bounded interval are widely used for signal analysis, compression, and for numerical solution of differential equations. We show that for many cases using the basis that we derive results in smaller error than the commonly used alternative.},
author = {Josefine Holm and Thomas Arildsen and M Nielsen and {L{\o}nsmann Nielsen}, Steffen},
date-added = {2021-09-20 08:28:09 +0200},
date-modified = {2021-09-20 08:28:09 +0200},
doi = {10.1007/s42452-020-03858-w},
issn = {2523-3971},
journal = {SN Applied Sciences},
language = {English},
month = nov,
number = {12},
publisher = {Springer Nature},
title = {Orthonormal, Moment Preserving Boundary Wavelet Scaling Functions in Python},
volume = {2},
year = {2020},
bdsk-url-1 = {https://doi.org/10.1007/s42452-020-03858-w}
}
@article{3573bdc123e84116819b6088316325d1,
abstract = {The lifetime of an Internet of Things (IoT) system consisting of battery-powered devices can be increased by minimizing the number of transmissions per device while not excessively deteriorating the correctness of the overall IoT monitoring. We propose a graph signal processing based algorithm for partitioning the sensor nodes into disjoint sampling sets. The sets can be sampled on a round-robin basis and each one contains enough information to reconstruct the entire signal within an acceptable error bound. Simulations on different models of graphs, based on graph theory and on real-world applications, show that our proposal consistently outperforms state-of-the-art sampling schemes, with no additional computational burden.},
author = {Josefine Holm and Federico Chiariotti and M Nielsen and Petar Popovski},
date-added = {2021-09-20 08:27:27 +0200},
date-modified = {2021-09-20 08:27:27 +0200},
doi = {10.1109/LCOMM.2021.3085023},
issn = {1089-7798},
journal = {I E E E Communications Letters},
keywords = {Base stations, Covariance matrices, Graph signal processing, Heuristic algorithms, Internet of Things, Interpolation, Partitioning algorithms, Signal processing, sampling set selection},
language = {English},
month = aug,
number = {8},
pages = {2763--2767},
publisher = {IEEE Computer Society Press},
title = {Lifetime Maximization of an Internet of Things (IoT) Network based on Graph Signal Processing},
volume = {25},
year = {2021},
bdsk-url-1 = {https://doi.org/10.1109/LCOMM.2021.3085023}
}
@article{MR3843555,
author = {Nielsen, Morten and Rasmussen, Morten Grud},
date-added = {2021-09-20 08:14:14 +0200},
date-modified = {2021-09-20 08:14:14 +0200},
doi = {10.7146/math.scand.a-103316},
fjournal = {Mathematica Scandinavica},
issn = {0025-5521},
journal = {Math. Scand.},
mrclass = {42B25 (46E40 47G10)},
mrnumber = {3843555},
mrreviewer = {Jian Tan},
number = {1},
pages = {72--84},
title = {Projection operators on matrix weighted {$L^p$} and a simple sufficient {M}uckenhoupt condition},
url = {https://doi-org.zorac.aub.aau.dk/10.7146/math.scand.a-103316},
volume = {123},
year = {2018},
bdsk-url-1 = {https://doi-org.zorac.aub.aau.dk/10.7146/math.scand.a-103316},
bdsk-url-2 = {https://doi.org/10.7146/math.scand.a-103316}
}
@article{MR3981799,
author = {Cleanthous, Galatia and Georgiadis, Athanasios G. and Nielsen, Morten},
date-added = {2021-09-20 08:10:47 +0200},
date-modified = {2021-09-20 08:10:47 +0200},
doi = {10.7146/math.scand.a-113031},
fjournal = {Mathematica Scandinavica},
issn = {0025-5521},
journal = {Math. Scand.},
mrclass = {42B25 (42B35)},
mrnumber = {3981799},
mrreviewer = {Yueping Zhu},
number = {2},
pages = {289--304},
title = {Fourier multipliers on anisotropic mixed-norm spaces of distributions},
url = {https://doi-org.zorac.aub.aau.dk/10.7146/math.scand.a-113031},
volume = {124},
year = {2019},
bdsk-url-1 = {https://doi-org.zorac.aub.aau.dk/10.7146/math.scand.a-113031},
bdsk-url-2 = {https://doi.org/10.7146/math.scand.a-113031}
}
@article{MR4056434,
author = {Al-Jawahri, Zeineb and Nielsen, Morten},
date-added = {2021-09-20 08:09:22 +0200},
date-modified = {2021-09-20 08:09:22 +0200},
doi = {10.1002/mana.201700474},
fjournal = {Mathematische Nachrichten},
issn = {0025-584X},
journal = {Math. Nachr.},
mrclass = {42C15 (42B35 46F05)},
mrnumber = {4056434},
mrreviewer = {Padmavati},
number = {12},
pages = {2496--2521},
title = {On homogeneous decomposition spaces and associated decompositions of distribution spaces},
url = {https://doi-org.zorac.aub.aau.dk/10.1002/mana.201700474},
volume = {292},
year = {2019},
bdsk-url-1 = {https://doi-org.zorac.aub.aau.dk/10.1002/mana.201700474},
bdsk-url-2 = {https://doi.org/10.1002/mana.201700474}
}
@article{MR4256141,
author = {Al-Jawahri, Zeineb and Nielsen, Morten},
date-added = {2021-09-20 08:09:22 +0200},
date-modified = {2021-09-20 08:09:22 +0200},
doi = {10.1016/j.acha.2021.04.003},
fjournal = {Applied and Computational Harmonic Analysis. Time-Frequency and Time-Scale Analysis, Wavelets, Numerical Algorithms, and Applications},
issn = {1063-5203},
journal = {Appl. Comput. Harmon. Anal.},
mrclass = {42B35 (41A17 42C15)},
mrnumber = {4256141},
pages = {41--70},
title = {On a discrete transform of homogeneous decomposition spaces},
url = {https://doi-org.zorac.aub.aau.dk/10.1016/j.acha.2021.04.003},
volume = {55},
year = {2021},
bdsk-url-1 = {https://doi-org.zorac.aub.aau.dk/10.1016/j.acha.2021.04.003},
bdsk-url-2 = {https://doi.org/10.1016/j.acha.2021.04.003}
}
@article{MR3803735,
author = {Cleanthous, G. and Georgiadis, A. G. and Nielsen, M.},
date-added = {2021-09-20 08:09:22 +0200},
date-modified = {2021-09-20 08:09:22 +0200},
doi = {10.1007/s00009-018-1171-3},
fjournal = {Mediterranean Journal of Mathematics},
issn = {1660-5446},
journal = {Mediterr. J. Math.},
mrclass = {42B15 (42B25 42B35 46F10)},
mrnumber = {3803735},
mrreviewer = {Joaqu\'{\i}n Motos},
number = {3},
pages = {Paper No. 122, 14},
title = {Fourier multipliers on decomposition spaces of modulation and {T}riebel-{L}izorkin type},
url = {https://doi-org.zorac.aub.aau.dk/10.1007/s00009-018-1171-3},
volume = {15},
year = {2018},
bdsk-url-1 = {https://doi-org.zorac.aub.aau.dk/10.1007/s00009-018-1171-3},
bdsk-url-2 = {https://doi.org/10.1007/s00009-018-1171-3}
}
@article{MR3917042,
author = {Cleanthous, G. and Georgiadis, A. G. and Nielsen, M.},
date-added = {2021-09-20 08:09:22 +0200},
date-modified = {2021-09-20 08:09:22 +0200},
doi = {10.1007/s00605-018-1251-2},
fjournal = {Monatshefte f\"{u}r Mathematik},
issn = {0026-9255},
journal = {Monatsh. Math.},
mrclass = {42A16 (30B30 30B40 30H10 30H25 42A05 42A45)},
mrnumber = {3917042},
mrreviewer = {Ciqiang Zhuo},
number = {3},
pages = {467--493},
title = {Molecular decomposition and {F}ourier multipliers for holomorphic {B}esov and {T}riebel-{L}izorkin spaces},
url = {https://doi-org.zorac.aub.aau.dk/10.1007/s00605-018-1251-2},
volume = {188},
year = {2019},
bdsk-url-1 = {https://doi-org.zorac.aub.aau.dk/10.1007/s00605-018-1251-2},
bdsk-url-2 = {https://doi.org/10.1007/s00605-018-1251-2}
}
@article{MR3830624,
author = {Georgiadis, Athanasios G. and Nielsen, Morten},
date-added = {2021-09-20 08:09:22 +0200},
date-modified = {2021-09-20 08:09:22 +0200},
doi = {10.1016/j.jat.2018.04.013},
fjournal = {Journal of Approximation Theory},
issn = {0021-9045},
journal = {J. Approx. Theory},
mrclass = {58J35 (43A15 43A85 46E35 46F05 58J40)},
mrnumber = {3830624},
mrreviewer = {Raffaela Capitanelli},
pages = {1--19},
title = {Spectral multipliers on spaces of distributions associated with non-negative self-adjoint operators},
url = {https://doi-org.zorac.aub.aau.dk/10.1016/j.jat.2018.04.013},
volume = {234},
year = {2018},
bdsk-url-1 = {https://doi-org.zorac.aub.aau.dk/10.1016/j.jat.2018.04.013},
bdsk-url-2 = {https://doi.org/10.1016/j.jat.2018.04.013}
}
@article{MR4017862,
author = {Nielsen, Morten and \v{S}iki\'{c}, Hrvoje},
date-added = {2021-09-20 08:09:22 +0200},
date-modified = {2021-09-20 08:09:22 +0200},
doi = {10.1017/s0013091519000038},
fjournal = {Proceedings of the Edinburgh Mathematical Society. Series II},
issn = {0013-0915},
journal = {Proc. Edinb. Math. Soc. (2)},
mrclass = {42B25 (42B35)},
mrnumber = {4017862},
mrreviewer = {Carlos Mudarra},
number = {4},
pages = {1017--1031},
title = {Muckenhoupt class weight decomposition and {BMO} distance to bounded functions},
url = {https://doi-org.zorac.aub.aau.dk/10.1017/s0013091519000038},
volume = {62},
year = {2019},
bdsk-url-1 = {https://doi-org.zorac.aub.aau.dk/10.1017/s0013091519000038},
bdsk-url-2 = {https://doi.org/10.1017/s0013091519000038}
}
@article{MR4302200,
author = {Nielsen, Morten and \v{S}iki\'{c}, Hrvoje},
date-added = {2021-09-20 08:09:22 +0200},
date-modified = {2021-09-20 08:09:22 +0200},
doi = {10.1007/s12220-020-00440-z},
fjournal = {Journal of Geometric Analysis},
issn = {1050-6926},
journal = {J. Geom. Anal.},
mrclass = {42B25 (15B48 42B35 47B47)},
mrnumber = {4302200},
number = {9},
pages = {8850--8865},
title = {Muckenhoupt {M}atrix {W}eights},
url = {https://doi-org.zorac.aub.aau.dk/10.1007/s12220-020-00440-z},
volume = {31},
year = {2021},
bdsk-url-1 = {https://doi-org.zorac.aub.aau.dk/10.1007/s12220-020-00440-z},
bdsk-url-2 = {https://doi.org/10.1007/s12220-020-00440-z}
}
@article{MR3843849,
author = {Ottosen, Emil {S}olsb{\ae}k and Nielsen, Morten},
date-added = {2021-09-20 08:09:22 +0200},
date-modified = {2021-09-20 08:36:09 +0200},
doi = {10.1007/s00041-017-9546-6},
fjournal = {The Journal of Fourier Analysis and Applications},
issn = {1069-5869},
journal = {J. Fourier Anal. Appl.},
mrclass = {42B35 (41A17 41A46 42C15)},
mrnumber = {3843849},
mrreviewer = {Yoshihiro Sawano},
number = {4},
pages = {1048--1071},
title = {A characterization of sparse nonstationary {G}abor expansions},
url = {https://doi-org.zorac.aub.aau.dk/10.1007/s00041-017-9546-6},
volume = {24},
year = {2018},
bdsk-url-1 = {https://doi-org.zorac.aub.aau.dk/10.1007/s00041-017-9546-6},
bdsk-url-2 = {https://doi.org/10.1007/s00041-017-9546-6}
}
@article{MR3981281,
author = {Cleanthous, Galatia and Georgiadis, Athanasios G. and Nielsen, Morten},
date-added = {2020-02-10 14:02:14 +0100},
date-modified = {2020-02-10 14:02:14 +0100},
doi = {10.1016/j.acha.2017.10.001},
fjournal = {Applied and Computational Harmonic Analysis. Time-Frequency and Time-Scale Analysis, Wavelets, Numerical Algorithms, and Applications},
issn = {1063-5203},
journal = {Appl. Comput. Harmon. Anal.},
mrclass = {42B35 (35S05 42B15 42B25 42C40 46E35 46F10 47G30)},
mrnumber = {3981281},
mrreviewer = {Mario Milman},
number = {2},
pages = {447--480},
title = {Molecular decomposition of anisotropic homogeneous mixed-norm spaces with applications to the boundedness of operators},
url = {https://doi.org/10.1016/j.acha.2017.10.001},
volume = {47},
year = {2019},
bdsk-url-1 = {https://doi.org/10.1016/j.acha.2017.10.001}
}
@article{MR3824122,
author = {Jacobsen, R. D. and M{\o}ller, J. and Nielsen, M. and G. Rasmussen, M.},
bib2html_dl_html = {https://doi.org/10.1016/j.acha.2017.09.004},
bib2html_pubtype = {Journal Article},
date-added = {2019-03-04 15:45:24 +0100},
date-modified = {2019-03-04 15:47:06 +0100},
fjournal = {Applied and Computational Harmonic Analysis. Time-Frequency and Time-Scale Analysis, Wavelets, Numerical Algorithms, and Applications},
issn = {1063-5203},
journal = {Appl. Comput. Harmon. Anal.},
mrclass = {94A20 (60G55)},
mrnumber = {3824122},
number = {2},
pages = {453--461},
title = {Investigations of the effects of random sampling schemes on the stability of generalized sampling},
volume = {45},
year = {2018},
bdsk-url-1 = {https://doi.org/10.1016/j.acha.2017.09.004}
}
@article{Ottosen2017,
abstract = {We consider sparseness properties of adaptive time-frequency representations obtained using nonstationary Gabor frames (NSGFs). NSGFs generalize classical Gabor frames by allowing for adaptivity in either time or frequency. It is known that the concept of painless nonorthogonal expansions generalizes to the nonstationary case, providing perfect reconstruction and an FFT based implementation for compactly supported window functions sampled at a certain density. It is also known that for some signal classes, NSGFs with flexible time resolution tend to provide sparser expansions than can be obtained with classical Gabor frames. In this article we show, for the continuous case, that sparseness of a nonstationary Gabor expansion is equivalent to smoothness in an associated decomposition space. In this way we characterize signals with sparse expansions relative to NSGFs with flexible time resolution. Based on this characterization we prove an upper bound on the approximation error occurring when thresholding the coefficients of the corresponding frame expansions. We complement the theoretical results with numerical experiments, estimating the rate of approximation obtained from thresholding the coefficients of both stationary and nonstationary Gabor expansions.},
author = {Ottosen, E. S. and Nielsen, M.},
bib2html_dl_html = {https://doi.org/10.1007/s10444-017-9577-1},
bib2html_pubtype = {Journal Article},
date-added = {2018-05-30 08:57:14 +0000},
date-modified = {2019-03-04 15:16:27 +0100},
day = {26},
issn = {1572-9044},
journal = {Advances in Computational Mathematics},
number = {4},
pages = {1183-1203},
title = {Nonlinear approximation with nonstationary Gabor frames},
volume = {44},
year = {2018},
bdsk-url-1 = {https://doi.org/10.1007/s10444-017-9577-1}
}
@article{Georgiadis2017,
author = {Georgiadis, A. G. and Johnsen, J. and Nielsen, M.},
bib2html_dl_html = {https://doi.org/10.1007/s00605-017-1036-z},
bib2html_pubtype = {Journal Article},
date-added = {2017-09-22 11:29:30 +0000},
date-modified = {2019-03-04 15:24:08 +0100},
day = {01},
issn = {1436-5081},
journal = {Monatshefte f{\"u}r Mathematik},
number = {4},
pages = {587--624},
title = {Wavelet transforms for homogeneous mixed-norm Triebel--Lizorkin spaces},
volume = {183},
year = {2017},
bdsk-url-1 = {https://doi.org/10.1007/s00605-017-1036-z},
bdsk-url-2 = {http://dx.doi.org/10.1007/s00605-017-1036-z}
}
@article{Jacobsen:2016aa,
author = {Jacobsen, {C. R. D.} and Nielsen, M. and Rasmussen, {M. G.}},
bib2html_dl_pdf = {http://doi.org/10.5334/jors.157},
bib2html_pubtype = {Journal Article},
date-added = {2017-02-28 13:55:58 +0000},
date-modified = {2017-09-22 11:40:00 +0000},
journal = {Journal of Open Research Software},
number = {1},
pages = {12 pp.},
title = {Generalized sampling in Julia},
volume = {5},
year = {2017}
}
@inproceedings{Cleanthous:2016ab,
author = {Cleanthous, G. and Georgiadis, A. G. and Nielsen, M.},
bib2html_dl_pdf = {http://vbn.aau.dk/files/244946561/AGetal.pdf},
bib2html_pubtype = {Refereed Conference},
booktitle = {Proceedings of the 15th Panhellenic Conference of Mathematical Analysis},
date-added = {2017-02-28 13:46:51 +0000},
date-modified = {2017-02-28 15:17:09 +0000},
pages = {29--38},
publisher = {University of Crete},
title = {Spaces of distributions with mixed Lebesgue norms},
year = {2016}
}
@article{Nielsen:2016aa,
author = {Nielsen, Morten},
bib2html_dl_html = {http://dx.doi.org/10.1216/RMJ-2016-46-6-2043},
bib2html_pubtype = {Journal Article},
date-added = {2017-02-28 13:30:48 +0000},
date-modified = {2017-02-28 14:56:55 +0000},
fjournal = {The Rocky Mountain Journal of Mathematics},
issn = {0035-7596},
journal = {Rocky Mountain J. Math.},
mrclass = {42C15 (42C40 46B15)},
mrnumber = {3591271},
number = {6},
pages = {2043--2060},
title = {On {S}chauder basis properties of multiply generated {G}abor systems},
volume = {46},
year = {2016},
bdsk-url-1 = {http://dx.doi.org/10.1216/RMJ-2016-46-6-2043}
}
@article{Nielsen:2015aa,
author = {Nielsen, Morten},
bib2html_dl_html = {http://dx.doi.org/10.3336/gm.50.1.11},
bib2html_pubtype = {Journal Article},
date-added = {2017-02-28 13:27:46 +0000},
date-modified = {2017-02-28 14:56:55 +0000},
fjournal = {Glasnik Matemati\v cki. Serija III},
issn = {0017-095X},
journal = {Glas. Mat. Ser. III},
mrclass = {42C15 (41A60 42C10)},
mrnumber = {3361271},
mrreviewer = {Krishnan Parthasarathy},
number = {1},
pages = {193--205},
title = {On quasi-greedy bases associated with unitary representations of countable groups},
volume = {50(70)},
year = {2015},
bdsk-url-1 = {http://dx.doi.org/10.3336/gm.50.1.11}
}
@article{Georgiadis:2016aa,
author = {Georgiadis, A. G. and Nielsen, M.},
bib2html_dl_html = {http://dx.doi.org/10.1002/mana.201500390},
bib2html_pubtype = {Journal Article},
date-added = {2017-02-28 13:12:11 +0000},
date-modified = {2017-02-28 14:56:55 +0000},
fjournal = {Mathematische Nachrichten},
issn = {0025-584X},
journal = {Math. Nachr.},
mrclass = {47F05 (35S05 46E35)},
mrnumber = {3573690},
mrreviewer = {G. V. Rozenblum},
number = {16},
pages = {2019--2036},
title = {Pseudodifferential operators on mixed-norm {B}esov and {T}riebel-{L}izorkin spaces},
volume = {289},
year = {2016},
bdsk-url-1 = {http://dx.doi.org/10.1002/mana.201500390}
}
@article{Cleanthous:2016aa,
author = {Cleanthous, G. and Georgiadis, A. G. and Nielsen, M.},
bib2html_dl_pdf = {http://dx.doi.org/10.1090/conm/693},
bib2html_pubtype = {Journal Article},
date-added = {2016-08-29 10:25:40 +0000},
date-modified = {2017-09-22 11:15:43 +0000},
journal = {Contemporary Mathematics},
pages = {167-184},
title = {Discrete decomposition of homogeneous mixed-norm Besov spaces},
volume = {693},
year = {2017}
}
@article{Georgiadis:2016ab,
abstract = {We consider H{\"o}rmander type symbols on a family of spaces associated with non-negative self-adjoint operators, and we prove boundedness of the corresponding pseudodifferential operators on both classical and non-classical Besov and Triebel--Lizorkin spaces. Consequently, this also covers the case of Sobolev spaces. As an application, we obtain boundedness of spectral multipliers on the mentioned spaces.},
author = {Georgiadis, A. G. and Nielsen, M.},
bib2html_dl_pdf = {http://link.springer.com/article/10.1007/s00041-016-9472-z},
bib2html_pubtype = {Journal Article},
date-added = {2016-08-29 08:32:37 +0000},
date-modified = {2019-03-04 15:22:32 +0100},
issn = {1531-5851},
journal = {Journal of Fourier Analysis and Applications},
number = {3},
pages = {344-378},
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