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
- Mean value operators and Radon transforms
Refereed book chapters
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
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,
Contemporary Mathematics, Vol. 598 (2013), 97-110
Multi-window Gabor frames in amalgam spaces,
w. R. Balan, I.A. Krishtal, K. Okoudjou
and J.L. Romero, Math. Res. Lett., Vol. 21, Number 1 (2014), 55-69
New atomic decompositions for Bergman spaces on the unit ball,
w. K. Grochenig and G. Olafsson, Indiana Univ. Math. J., Vol. 66, Issue 1 (2017), 205-235
Surjectivity of mean value operators on noncompact symmetric spaces,
w. F. Gonzalez and T. Kakehi in J. Funct. Anal. 272 (2017), no. 9, 3610-3646.
Atomic decompositions of mixed norm Bergman spaces on tube type domains ,
accepted into an AMS Contemporary Mathematics volume.
Coorbits for projective representations with an application to Bergman spaces
w. A. Darweesh and G. Olafsson, submitted.
Sampling in Euclidean and Non-Euclidean Domains: A Unified Approach,
w. S. Casey, Chapter in Applied and Numerical Harmonic Analysis book series
Sampling Theory, a Renaissance. Birkhauser, Boston (2015).
Sampling in spaces of bandlimited functions on commutative spaces,
w. G. Olafsson. Chapter in Applied and Numerical Harmonic Analysis book series
Excursions in Harmonic Analysis, Volume 1. Birkhauser, Boston (2012).
Geometric Analysis and Integral Geometry, Contemporary Mathematics, Volume 598 (2013),
proceedings of 2012 AMS
special session honoring Sigurdur Helgason and Tufts Workshop on this topic. Editors: Todd Quinto (main editor),
Fulton Gonzalez and Jens Christensen
Trends in harmonic analysis and its applications,
Contemporary Mathematics, Volume 650 (2015),
Proceedings of AMS special session at 2014 Spring Eastern Sectional Meeting at UMBC in Baltimore.
Editors: Jens Christensen (main editor), Susanna Dann, Azita Mayeli and Gestur Olafsson