caa a22 4500 463246721 CHVBK 20180405153328.0 cr unu---uuuuu 170326e20070201xx s 000 0 eng 10.1007/s00041-006-6024-y doi (NATIONALLICENCE)springer-10.1007/s00041-006-6024-y Frame Decomposition of Decomposition Spaces [Elektronische Daten] [Lasse Borup, Morten Nielsen] A new construction of tight frames for $L_2({\Bbb R}^d)$ with flexible time-frequency localization is considered. The frames can be adapted to form atomic decompositions for a large family of smoothness spaces on ${\Bbb R}^d,$ a class of so-called decomposition spaces. The decomposition space norm can be completely characterized by a sparseness condition on the frame coefficients. As examples of the general construction, new tight frames yielding decompositions of Besov space, anisotropic Besov spaces, α-modulation spaces, and anisotropic α-modulation spaces are considered. Finally, curvelet-type tight frames are constructed on ${\Bbb R}^d, d \geq 2.$ Birkhauser Boston, 2007 Borup Lasse Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220, Aalborg East, Denmark aut Nielsen Morten Department of Mathematics, Washington University, Campus Box 1146, St. Louis, MO 63130 and Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220, Aalborg East, Denmark aut Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/1(2007-02-01), 39-70 1069-5869 13:1<39 2007 13 41 https://doi.org/10.1007/s00041-006-6024-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00041-006-6024-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Borup Lasse Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220, Aalborg East, Denmark aut NATIONALLICENCE 700 1- Nielsen Morten Department of Mathematics, Washington University, Campus Box 1146, St. Louis, MO 63130 and Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220, Aalborg East, Denmark aut NATIONALLICENCE 773 0- Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/1(2007-02-01), 39-70 1069-5869 13:1<39 2007 13 41 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer