My current research is concerned with the construction
of Banach spaces by use of representation theory
and discrete decomposition of these spaces.
- Harmonic analysis
- Time-frequency analysis
- Representation theory
- Uncertainty principles
- Frames and wavelets
- Reproducing kernel Banach spaces
- Sampling theory
The Uncertainty Principle for Operators Determined by Lie Groups
, J. Fourier Anal. Appl. 10 (2004), no. 5, 541--544.
An uncertainty principle related to the Euclidean motion group
, w. H. Schlichtkrull, Math. Proc. R. Ir. Acad. 104A (2004), no. 2, 249--252 (electronic)
Examples of Coorbit Spaces for Dual Pairs
, w. G. Olafsson, Acta Appl. Math. 107 (2009), no. 1-3, 25--48.
Coorbit Spaces for Dual Pairs,
w. G. Olafsson, Appl. Comp. Harm. Anal. Vol. 31 Issue 2 (2011), 303-324
Sampling in reproducing kernel Banach spaces on Lie groups,
Journal of Approximation Theory, Vol. 164 Issue 1 (2012), 179-203
Sampling in spaces of bandlimited functions on commutative spaces (ArXiV),
w. G. Olafsson, chapter in ANHA book series, 2012
Multi-window Gabor frames in amalgam spaces (ArXiV),
w. R. Balan, I.A. Krishtal, K. Okoudjou
and J.L. Romero, Submitted, August 2011
Coorbit description and atomic decomposition of Besov spaces,
w. A. Mayeli and G. Olafsson,
Numer. Funct. Anal. Optim., Vol. 33, Issue 7-9 (2012), 847-871
Atomic decompositions of Besov spaces related to symmetric cones (ArXiV),
To appear in Contemporary Mathematics
Geometric Analysis and Integral Ieometry, proceedings of 2012 AMS
special session honoring Sigurdur Helgason and Tufts Workshop on this topic,
approved by AMS for the series Contemporary Mathematics.