| [1] |
M. Nielsen.
On a conjecture about Schauder-basis properties of the Daubechies
wavelet packets.
Appl. Comput. Harmon. Anal., 87:Paper No. 101938, 2027. [ bib | DOI | http ] |
| [2] |
M. Nielsen and H. Šikić.
Matrix weights on compact and non-compact domains.
J. Math. Anal. Appl., 555(2):Paper No. 130069, 23, 2026. [ bib | DOI | http ] |
| [3] |
M. Nielsen.
Painless construction of unconditional bases for anisotropic
modulation and Triebel-Lizorkin type spaces.
Appl. Comput. Harmon. Anal., 82:Paper No. 101832, 25, 2026. [ bib | DOI | http ] |
| [4] |
M. Nielsen.
Matrix Ap-weights relative to a pseudo-metric.
J. Geom. Anal., 36(9):Paper No. 293, 37, 2026. [ bib | DOI | http ] |
| [5] |
M. Nielsen.
Bandlimited multipliers on matrix-weighted Lp-spaces.
J. Fourier Anal. Appl., 31(1):Paper No. 3, 10, 2025. [ bib | DOI | http ] |
| [6] |
M. Nielsen.
Matrix weighted α-modulation spaces.
Monatsh. Math., 206(2):419–448, 2025. [ bib | DOI | http ] |
| [7] |
M. Nielsen.
Discrete decomposition of mixed-norm α-modulation spaces.
Int. J. Wavelets Multiresolut. Inf. Process., 23(1):Paper No.
2450038, 26, 2025. [ bib | DOI | http ] |
| [8] |
M. Nielsen and H. Šikić.
Muckenhoupt matrix weights for general bases.
In The mathematical heritage of Guido Weiss, Appl. Numer.
Harmon. Anal., pages 361–386. Birkhäuser/Springer, Cham, 2025. [ bib | DOI | http ] |
| [9] |
M. Nielsen.
Pseudodifferential operators on mixed-norm α-modulation
spaces.
Rocky Mountain J. Math., 53(3):875–887, 2023. [ bib | DOI | http ] |
| [10] |
M. Nielsen.
Stable decomposition of homogeneous mixed-norm Triebel-Lizorkin
spaces.
J. Approx. Theory, 295:Paper No. 105958, 28, 2023. [ bib | DOI | http ] |
| [11] |
R. Gribonval, G. Kutyniok, M. Nielsen, and F. Voigtlaender.
Approximation spaces of deep neural networks.
Constr. Approx., 55(1):259–367, 2022. [ bib | DOI | http ] |
| [12] |
M. Nielsen.
Unconditional bases for homogeneous α-modulation type
spaces.
Mediterr. J. Math., 19(2):Paper No. 55, 18, 2022. [ bib | DOI | http ] |
| [13] |
J. Holm, F. Chiariotti, M. Nielsen, and P. Popovski.
Lifetime maximization of an internet of things (iot) network based on
graph signal processing.
I E E E Communications Letters, 25(8):2763–2767, Aug. 2021. [ bib | DOI ] |
| [14] |
M. Nielsen and H. Šikić.
Muckenhoupt Matrix Weights.
J. Geom. Anal., 31(9):8850–8865, 2021. [ bib | DOI | http ] |
| [15] |
Z. Al-Jawahri and M. Nielsen.
On a discrete transform of homogeneous decomposition spaces.
Appl. Comput. Harmon. Anal., 55:41–70, 2021. [ bib | DOI | http ] |
| [16] |
J. Holm, T. Arildsen, M. Nielsen, and S. Lønsmann Nielsen.
Orthonormal, moment preserving boundary wavelet scaling functions in
python.
SN Applied Sciences, 2(12), Nov. 2020. [ bib | DOI ] |
| [17] |
G. Cleanthous, A. G. Georgiadis, and M. Nielsen.
Molecular decomposition of anisotropic homogeneous mixed-norm spaces
with applications to the boundedness of operators.
Appl. Comput. Harmon. Anal., 47(2):447–480, 2019. [ bib | DOI | http ] |
| [18] |
M. Nielsen and H. Šikić.
Muckenhoupt class weight decomposition and BMO distance to bounded
functions.
Proc. Edinb. Math. Soc. (2), 62(4):1017–1031, 2019. [ bib | DOI | http ] |
| [19] |
G. Cleanthous, A. G. Georgiadis, and M. Nielsen.
Molecular decomposition and Fourier multipliers for holomorphic
Besov and Triebel-Lizorkin spaces.
Monatsh. Math., 188(3):467–493, 2019. [ bib | DOI | http ] |
| [20] |
Z. Al-Jawahri and M. Nielsen.
On homogeneous decomposition spaces and associated decompositions of
distribution spaces.
Math. Nachr., 292(12):2496–2521, 2019. [ bib | DOI | http ] |
| [21] |
G. Cleanthous, A. G. Georgiadis, and M. Nielsen.
Fourier multipliers on anisotropic mixed-norm spaces of
distributions.
Math. Scand., 124(2):289–304, 2019. [ bib | DOI | http ] |
| [22] |
J. Møller, M. Nielsen, E. Porcu, and E. Rubak.
Determinantal point process models on the sphere.
Bernoulli, 24(2):1171–1201, 2018. [ bib | arXiv | http ] |
| [23] |
E. S. Ottosen and M. Nielsen.
Nonlinear approximation with nonstationary gabor frames.
Advances in Computational Mathematics, 44(4):1183–1203, 2018. [ bib | http ] |
| [24] |
R. D. Jacobsen, J. Møller, M. Nielsen, and M. G. Rasmussen.
Investigations of the effects of random sampling schemes on the
stability of generalized sampling.
Appl. Comput. Harmon. Anal., 45(2):453–461, 2018. [ bib | http ] |
| [25] |
E. S. Ottosen and M. Nielsen.
A characterization of sparse nonstationary Gabor expansions.
J. Fourier Anal. Appl., 24(4):1048–1071, 2018. [ bib | DOI | http ] |
| [26] |
A. G. Georgiadis and M. Nielsen.
Spectral multipliers on spaces of distributions associated with
non-negative self-adjoint operators.
J. Approx. Theory, 234:1–19, 2018. [ bib | DOI | http ] |
| [27] |
G. Cleanthous, A. G. Georgiadis, and M. Nielsen.
Fourier multipliers on decomposition spaces of modulation and
Triebel-Lizorkin type.
Mediterr. J. Math., 15(3):Paper No. 122, 14, 2018. [ bib | DOI | http ] |
| [28] |
M. Nielsen and M. G. Rasmussen.
Projection operators on matrix weighted Lp and a simple
sufficient Muckenhoupt condition.
Math. Scand., 123(1):72–84, 2018. [ bib | DOI | http ] |
| [29] |
A. G. Georgiadis and M. Nielsen.
Pseudodifferential operators on spaces of distributions associated
with non-negative self-adjoint operators.
Journal of Fourier Analysis and Applications, 23(3):344–378,
2017. [ bib | http ] |
| [30] |
G. Cleanthous, A. G. Georgiadis, and M. Nielsen.
Discrete decomposition of homogeneous mixed-norm besov spaces.
Contemporary Mathematics, 693:167–184, 2017. [ bib | http ] |
| [31] |
C. Jacobsen, M. Nielsen, and M. Rasmussen.
Generalized sampling in julia.
Journal of Open Research Software, 5(1):12 pp., 2017. [ bib | http ] |
| [32] |
A. G. Georgiadis, J. Johnsen, and M. Nielsen.
Wavelet transforms for homogeneous mixed-norm triebel–lizorkin
spaces.
Monatshefte für Mathematik, 183(4):587–624, 2017. [ bib | http ] |
| [33] |
G. Cleanthous, A. G. Georgiadis, and M. Nielsen.
Anisotropic mixed-norm Hardy spaces.
J. Geom. Anal., 27(4):2758–2787, 2017. [ bib | DOI | http ] |
| [34] |
A. G. Georgiadis and M. Nielsen.
Pseudodifferential operators on mixed-norm Besov and
Triebel-Lizorkin spaces.
Math. Nachr., 289(16):2019–2036, 2016. [ bib | http ] |
| [35] |
M. Nielsen.
On Schauder basis properties of multiply generated Gabor systems.
Rocky Mountain J. Math., 46(6):2043–2060, 2016. [ bib | http ] |
| [36] |
G. Cleanthous, A. G. Georgiadis, and M. Nielsen.
Spaces of distributions with mixed lebesgue norms.
In Proceedings of the 15th Panhellenic Conference of
Mathematical Analysis, pages 29–38. University of Crete, 2016. [ bib | .pdf ] |
| [37] |
M. Nielsen.
On quasi-greedy bases associated with unitary representations of
countable groups.
Glas. Mat. Ser. III, 50(70)(1):193–205, 2015. [ bib | http ] |
| [38] |
R. Jacobsen and M. Nielsen.
Investigation of the effects of data collection on visual stylometry.
International Journal of Image and Graphics, 14(4):1450020,
2014. [ bib | http ] |
| [39] |
M. Nielsen.
Frames for decomposition spaces generated by a single function.
Collect. Math., 65(2):183–201, 2014. [ bib | .pdf ] |
| [40] |
M. Nielsen and H. Sikic.
On stability of schauder bases of integer translates.
J. Funct. Anal., 266(4):2281–2293, 2014. [ bib | .pdf ] |
| [41] |
R. Gribonval and M. Nielsen.
The restricted isometry property meets nonlinear approximation with
redundant frames.
J. Approx. Theory, 165(1):1–19, 2013. [ bib | http | .pdf ] |
| [42] |
E. Hernandez, M. Nielsen, H. Sikic, and F. Soria.
Democratic systems of translates.
J. Approx. Theory, 171:105–127, 2013. [ bib | http ] |
| [43] |
R. Jacobsen and M. Nielsen.
Stylometry of paintings using hidden markov modelling of contourlet
transforms.
Signal Processing, 93(3):579–591, 2013. [ bib | http | .pdf ] |
| [44] |
M. Nielsen.
On traces of general decomposition spaces.
Monatsh. Math., 171(3-4):443–457, 2013. [ bib | http ] |
| [45] |
M. Nielsen and H. Sikic.
Maximal functions, product condition and its eccentricity.
Collect. Math., 63(2):192–202, 2012. [ bib | http | .pdf ] |
| [46] |
M. Nielsen.
On transference of multipliers on matrix weighted Lp-spaces.
J. Geom. Anal., 22(1):12–22, 2012. [ bib | http | .pdf ] |
| [47] |
K. N. Rasmussen and M. Nielsen.
Compactly supported curvelet-type systems.
J. Funct. Spaces Appl., pages Art. ID 876315, pp. 18, 2012. [ bib | http | .pdf ] |
| [48] |
M. Nielsen and K. N. Rasmussen.
Compactly supported frames for decomposition spaces.
J. Fourier Anal. Appl., 18(1):87–117, 2012. [ bib | http | .pdf ] |
| [49] |
M. Nielsen.
On stability of finitely generated shift-invariant systems.
J. Fourier Anal. Appl., 16(6):901–920, 2010. [ bib | .pdf ] |
| [50] |
M. Nielsen.
Orthonormal bases for α-modulation spaces.
Collect. Math., 61(2):173–190, 2010. [ bib | .pdf ] |
| [51] |
M. Nielsen.
Trigonometric bases for matrix weighted Lp-spaces.
J. Math. Anal. Appl., 371:784–792, 2010. [ bib | .pdf ] |
| [52] |
M. Nielsen.
Trigonometric quasi-greedy bases for Lp([0,1]).
Rocky Mountain J. Math., 39(4):1267–1278, 2009. [ bib | .pdf ] |
| [53] |
M. Nielsen.
Aspects of nonlinear approximation with dictionaries.
Doctoral Thesis, Aalborg University, 2009. [ bib | .pdf ] |
| [54] |
R. Gribonval and M. Nielsen.
Beyond sparsity: recovering structured representations by l1
minimization and greedy algorithms.
Adv. Comput. Math., 28(1):23–41, 2008. [ bib | http ] |
| [55] |
L. Borup, R. Gribonval, and M. Nielsen.
Beyond coherence: recovering structured time-frequency
representations.
Appl. Comput. Harmon. Anal., 24(1):120–128, 2008. [ bib | http ] |
| [56] |
L. Borup and M. Nielsen.
On anisotropic Triebel-Lizorkin type spaces, with applications to
the study of pseudo-differential operators.
J. Funct. Spaces Appl., 6(2):107–154, 2008. [ bib | .pdf ] |
| [57] |
M. Nielsen and H. Sikic.
Quasi-greedy systems of integer translates.
J. Approx. Theory, 155(1):43–51, 2008. [ bib | .pdf ] |
| [58] |
L. Borup and M. Nielsen.
Frame decomposition of decomposition spaces.
J. Fourier Anal. Appl., 13(1):39–70, 2007. [ bib | .pdf ] |
| [59] |
R. Gribonval and M. Nielsen.
Highly sparse representations from dictionaries are unique and
independent of the sparseness measure.
Appl. Comput. Harmon. Anal., 22(3):335–355, 2007. [ bib | .pdf ] |
| [60] |
M. Nielsen.
On polynomial symbols for subdivision schemes.
Adv. Comput. Math., 27(2):195–209, 2007. [ bib | .pdf ] |
| [61] |
M. Nielsen and H. Sikic.
Schauder bases of integer translates.
Appl. Comput. Harmon. Anal., 23(2):259–262, 2007. [ bib | .pdf ] |
| [62] |
M. Nielsen.
An example of an almost greedy uniformly bounded orthonormal basis
for Lp(0,1).
J. Approx. Theory, 149(2):188–192, 2007. [ bib | .pdf ] |
| [63] |
L. Borup and M. Nielsen.
Nonlinear approximation in α-modulation spaces.
Math. Nachr., 279(1-2):101–120, 2006. [ bib | .pdf ] |
| [64] |
R. Gribonval and M. Nielsen.
Nonlinear approximation with dictionaries. II. Inverse estimates.
Constr. Approx., 24(2):157–173, 2006. [ bib | .ps ] |
| [65] |
L. Borup and M. Nielsen.
Banach frames for multivariate α-modulation spaces.
J. Math. Anal. Appl., 321(2):880–895, 2006. [ bib | .pdf ] |
| [66] |
L. Borup and M. Nielsen.
Boundedness for pseudodifferential operators on multivariate
α-modulation spaces.
Ark. Mat., 44(2):241–259, 2006. [ bib | .pdf ] |
| [67] |
L. Borup, R. Gribonval, and M. Nielsen.
Nonlinear approximation with bi-framelets.
In Approximation theory XI: Gatlinburg 2004, Mod. Methods
Math., pages 93–104. Nashboro Press, Brentwood, TN, 2005. [ bib | .pdf ] |
| [68] |
L. Borup and M. Nielsen.
Approximation with wave packets generated by a refinable function.
Proc. Amer. Math. Soc., 133(8):2409–2418 (electronic), 2005. [ bib | .pdf ] |
| [69] |
L. Borup and M. Nielsen.
On the equivalence of brushlet and wavelet bases.
J. Math. Anal. Appl., 309(1):117–135, 2005. [ bib | .pdf ] |
| [70] |
L. Borup and M. Nielsen.
Nonlinear approximation with general wave packets.
Anal. Theory Appl., 21(3):201–215, 2005. [ bib | .pdf ] |
| [71] |
M. Nielsen, L. Borup, and R. Gribonval.
Nonlinear approximation with redundant dictionaries.
In Proc. ICASSP' 05 (IEEE Conf. on Acoustics, Speech and Signal
Proc.), volume IV, pages 261–264, 2005. [ bib | .pdf ] |
| [72] |
R. Gribonval and M. Nielsen.
On approximation with spline generated framelets.
Constr. Approx., 20(2):207–232, 2004. [ bib | .ps ] |
| [73] |
R. Gribonval and M. Nielsen.
Nonlinear approximation with dictionaries. I. Direct estimates.
J. Fourier Anal. Appl., 10(1):51–71, 2004. [ bib | .pdf ] |
| [74] |
M. Nielsen.
Nonseparable Walsh-type functions on Rd.
Glas. Mat. Ser. III, 39(59)(1):111–138, 2004. [ bib | .pdf ] |
| [75] |
L. Borup, R. Gribonval, and M. Nielsen.
Bi-framelet systems with few vanishing moments characterize Besov
spaces.
Appl. Comput. Harmon. Anal., 17(1):3–28, 2004. [ bib | .pdf ] |
| [76] |
R. Gribonval and M. Nielsen.
On a problem of Gröchenig about nonlinear approximation with
localized frames.
J. Fourier Anal. Appl., 10(4):433–437, 2004. [ bib | .pdf ] |
| [77] |
L. Borup, R. Gribonval, and M. Nielsen.
Tight wavelet frames in Lebesgue and Sobolev spaces.
J. Funct. Spaces Appl., 2(3):227–252, 2004. [ bib | .ps ] |
| [78] |
R. Gribonval and M. Nielsen.
On the strong uniqueness of highly sparse expansions from redundant
dictionaries.
In Proc. Int Conf. Independent Component Analysis (ICA'04),
2004. [ bib | .pdf ] |
| [79] |
L. Borup and M. Nielsen.
Approximation with brushlet systems.
J. Approx. Theory, 123(1):25–51, 2003. [ bib | .ps ] |
| [80] |
R. Gribonval and M. Nielsen.
Sparse representations in unions of bases.
IEEE Trans. Inform. Theory, 49(12):3320–3325, 2003. [ bib | .pdf ] |
| [81] |
L. Borup and M. Nielsen.
Fast adaptive expansions in local trigonometric bases.
Signal Processing, 83(2):445–451, 2003. [ bib | .ps ] |
| [82] |
M. Nielsen and R. Gribonval.
Sparse decompositions in 'incoherent' dictionaries.
In Proc. IEEE Intl. Conf. on Image Proc. (ICIP'03), 2003. [ bib | .pdf ] |
| [83] |
R. Gribonval and M. Nielsen.
Approximation with highly redundant dictionaries.
In Proc. SPIE'03: 'Wavelets: Applications in Signal and Image
Processing', volume 5207, pages 216–227, 2003. [ bib | .ps ] |
| [84] |
M. Nielsen and R. Gribonval.
On the quasi-greedy property and uniformly bounded orthonormal
systems.
Technical report, Aalborg University, 2003. [ bib | .pdf ] |
| [85] |
L. Borup and M. Nielsen.
Some remarks on shrinkage operators.
Technical report, Aalborg University, 2003. [ bib | .ps ] |
| [86] |
M. Nielsen.
Highly nonstationary wavelet packets.
Appl. Comput. Harmon. Anal., 12(2):209–229, 2002. [ bib | .pdf ] |
| [87] |
M. Nielsen.
On convergence of wavelet packet expansions.
Approx. Theory Appl. (N.S.), 18(1):34–50, 2002. [ bib | .pdf ] |
| [88] |
L. Borup and M. Nielsen.
Nonseparable wavelet packets.
In Approximation theory, X (St. Louis, MO, 2001),
Innov. Appl. Math., pages 51–61. Vanderbilt Univ. Press, Nashville, TN,
2002. [ bib | .ps ] |
| [89] |
M. Nielsen and D.-X. Zhou.
Mean size of wavelet packets.
Appl. Comput. Harmon. Anal., 13(1):22–34, 2002. [ bib | .pdf ] |
| [90] |
M. Nielsen.
Size properties of wavelet packets generated using finite filters.
Rev. Mat. Iberoamericana, 18(2):249–265, 2002. [ bib | .pdf ] |
| [91] |
M. Nielsen.
On the construction and frequency localization of finite orthogonal
quadrature filters.
J. Approx. Theory, 108(1):36–52, 2001. [ bib | .pdf ] |
| [92] |
R. Gribonval and M. Nielsen.
Some remarks on non-linear approximation with Schauder bases.
East J. Approx., 7(3):267–285, 2001. [ bib | .pdf ] |
| [93] |
R. Gribonval and M. Nielsen.
Approximate weak greedy algorithms.
Adv. Comput. Math., 14(4):361–378, 2001. [ bib | .pdf ] |
| [94] |
M. Nielsen.
Walsh-type wavelet packet expansions.
Appl. Comput. Harmon. Anal., 9(3):265–285, 2000. [ bib | .pdf ] |
| [95] |
M. Nielsen.
Size Properties of Wavelet Packets.
PhD thesis, Washington University in St. Louis, 1999. [ bib | .pdf ] |
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