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Anisotropic wavelet bases and thresholding

Research output: Journal contributions › Journal articles › Research › peer-review

Standard

Anisotropic wavelet bases and thresholding. / Hochmuth, Reinhard.
In: Mathematische Nachrichten, Vol. 280, No. 5-6, 2007, p. 523-533.

Research output: Journal contributions › Journal articles › Research › peer-review

Harvard

Hochmuth, R 2007, 'Anisotropic wavelet bases and thresholding', Mathematische Nachrichten, vol. 280, no. 5-6, pp. 523-533. https://doi.org/10.1002/mana.200410500

APA

Hochmuth, R. (2007). Anisotropic wavelet bases and thresholding. Mathematische Nachrichten, 280(5-6), 523-533. https://doi.org/10.1002/mana.200410500

Vancouver

Hochmuth R. Anisotropic wavelet bases and thresholding. Mathematische Nachrichten. 2007;280(5-6):523-533. doi: 10.1002/mana.200410500

Bibtex

@article{bb7d2d6636484bb88cfb4ffaa449cc39,
title = "Anisotropic wavelet bases and thresholding",
abstract = "We consider thresholding with respect to anisotropic wavelet bases measuring the approximation error in anisotropic Hardy spaces H p a for p > 0, which are known to be equal to L p for p > 1. In particular, we characterize those functions that provide a specific convergence rate by intrinsic smoothness properties. To this end we apply restricted nonlinear approximation, see [3], which is a generalization of n-term approximation in which a weight function is used to control the terms of the approximations.",
keywords = "Mathematics, Anisotropic besov spaces, Anisotropic Hardy spaces, Anisotropic wavelet bases, Nonlinear approximation, Restricted nonlinear approximation, Thresholding, Wavelet shrinkage",
author = "Reinhard Hochmuth",
year = "2007",
doi = "10.1002/mana.200410500",
language = "English",
volume = "280",
pages = "523--533",
journal = "Mathematische Nachrichten",
issn = "1522-2616",
publisher = "Wiley-VCH Verlag",
number = "5-6",

}

RIS

TY - JOUR

T1 - Anisotropic wavelet bases and thresholding

AU - Hochmuth, Reinhard

PY - 2007

Y1 - 2007

N2 - We consider thresholding with respect to anisotropic wavelet bases measuring the approximation error in anisotropic Hardy spaces H p a for p > 0, which are known to be equal to L p for p > 1. In particular, we characterize those functions that provide a specific convergence rate by intrinsic smoothness properties. To this end we apply restricted nonlinear approximation, see [3], which is a generalization of n-term approximation in which a weight function is used to control the terms of the approximations.

AB - We consider thresholding with respect to anisotropic wavelet bases measuring the approximation error in anisotropic Hardy spaces H p a for p > 0, which are known to be equal to L p for p > 1. In particular, we characterize those functions that provide a specific convergence rate by intrinsic smoothness properties. To this end we apply restricted nonlinear approximation, see [3], which is a generalization of n-term approximation in which a weight function is used to control the terms of the approximations.

KW - Mathematics

KW - Anisotropic besov spaces

KW - Anisotropic Hardy spaces

KW - Anisotropic wavelet bases

KW - Nonlinear approximation

KW - Restricted nonlinear approximation

KW - Thresholding

KW - Wavelet shrinkage

UR - http://www.scopus.com/inward/record.url?scp=34247219773&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/ab9c7d13-c300-33c7-a014-b1cc6100111b/

U2 - 10.1002/mana.200410500

DO - 10.1002/mana.200410500

M3 - Journal articles

VL - 280

SP - 523

EP - 533

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

SN - 1522-2616

IS - 5-6

ER -

Related by journal

N-term approximation in anisotropic function spaces

Hochmuth, R., 2002, In: Mathematische Nachrichten. 244, 1, p. 131-149 19 p.

Research output: Journal contributions › Journal articles › Research › peer-review

The Cox ring of the space of complete rank two collineations

Hausen, J. & Liebendörfer, M., 06.2012, In: Mathematische Nachrichten. 285, 8-9, p. 974-980 7 p.

Research output: Journal contributions › Journal articles › Research › peer-review

Other publications by the same author(s)

Didactics of Mathematics in Higher Education as a Scientific Discipline - Conference Proceedings

Göller, R. (Editor), Biehler, R., Hochmuth, R. K. & Rück, H.-G., 2017, Kassel: Kompetenzentrum Hochschuldidaktik Mathematik - Universität Kassel. 509 p. (khdm-Report; vol. 2017, no. 05)

Research output: Books and anthologies › Conference proceedings › Research

Mathematik im Ingenieurwissenschaftsstudium – Ansätze zu einer fachbezogenen Kompetenzmodellierung

Hochmuth, R. K. & Schreiber, S., 2014, TeachING-LearnING.EU Tagungsband: movING Forward; Engineering Education from vision to mission. Tekkaya, A. E., Jeschke, S. & Petermann, M. (eds.). Technische Universität Dortmund, p. 68-76 9 p.

Research output: Contributions to collected editions/works › Article in conference proceedings › Research › peer-review

Mit Werkzeugen Mathematik und Stochastik lernen

Wassong, T., Frischemeier, D., Fischer, P. R., Hochmuth, R. & Bender, P., 2014, Wiesbaden: Springer Spektrum. 497 p.

Research output: Books and anthologies › Book

Vorstellung eines Fragebogens zur Erfassung von Lernstrategien in mathematikhaltigen Studiengängen.

Liebendörfer, M., Hochmuth, R. K., Schreiber, S., Göller, R., Kolter, J., Biehler, R., Kortemeyer, J. & Ostsieker, L., 2014, Beiträge zum Mathematikunterricht 2014: Beiträge zur 48. Jahrestagung der Gesellschaft für Didaktik der Mathematik vom 10. bis 14. März 2014 in Koblenz. Roth, J. & Ames, J. (eds.). WTM - Verlag für wissenschaftliche Texte und Medien, Vol. 2. p. 739-742 4 p.

Research output: Contributions to collected editions/works › Article in conference proceedings › Research

Blended-Learning Brückenkurs Mathematik für Wirtschaftswissenschaftler.

Goguadze, G. & Hochmuth, R., 25.11.2013, Mathematik im Übergang Schule / Hochschule und im ersten Studienjahr: Extended Abstracts zur 2. khdm-Arbeitstagung. Hoppenbrock, A., Schreiber, S., Göller, R., Biehler, R., Büchler, B., Hochmuth, R. & Rück, H.-G. (eds.). Universitätsbibliothek Kassel, Vol. khdm-Report 13-01. p. 63-64 2 p. (KHDM-Report; vol. 13, no. 01).

Research output: Contributions to collected editions/works › Other › Research

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