TY - JOUR

T1 - Compactly supported frames for decomposition spaces

A1 - Nielsen,Morten

A1 - Rasmussen,Kenneth Niemann

AU - Nielsen,Morten

AU - Rasmussen,Kenneth Niemann

PB - Birkhaeuser Boston

PY - 2012

Y1 - 2012

N2 - In this article we study a construction of compactly supported frame expansions for decomposition spaces of Triebel-Lizorkin type and for the associated modulation spaces. This is done by showing that finite linear combinations of shifts and dilates of a single function with sufficient decay in both direct and frequency space can constitute a frame for Triebel-Lizorkin type spaces and the associated modulation spaces. First, we extend the machinery of almost diagonal matrices to Triebel-Lizorkin type spaces and the associated modulation spaces. Next, we prove that two function systems which are sufficiently close have an almost diagonal “change of frame coefficient” matrix. Finally, we approximate to an arbitrary degree an already known frame for Triebel-Lizorkin type spaces and the associated modulation spaces with a single function with sufficient decay in both direct and frequency space.

AB - In this article we study a construction of compactly supported frame expansions for decomposition spaces of Triebel-Lizorkin type and for the associated modulation spaces. This is done by showing that finite linear combinations of shifts and dilates of a single function with sufficient decay in both direct and frequency space can constitute a frame for Triebel-Lizorkin type spaces and the associated modulation spaces. First, we extend the machinery of almost diagonal matrices to Triebel-Lizorkin type spaces and the associated modulation spaces. Next, we prove that two function systems which are sufficiently close have an almost diagonal “change of frame coefficient” matrix. Finally, we approximate to an arbitrary degree an already known frame for Triebel-Lizorkin type spaces and the associated modulation spaces with a single function with sufficient decay in both direct and frequency space.

U2 - 10.1007/s00041-011-9190-5

DO - 10.1007/s00041-011-9190-5

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

SN - 1069-5869

IS - 1

VL - 18

SP - 87

EP - 117

ER -