




Research
My current research is concerned with the construction
of Banach spaces by use of representation theory
and discrete decomposition of these spaces.
Research interests
 Harmonic analysis
 Timefrequency analysis
 Representation theory
 Uncertainty principles
 Frames and wavelets
 Reproducing kernel Banach spaces
 Sampling theory
 Mean value operators and Radon transforms
Publications
Articles

New atomic decompositions of Bergman spaces on bounded symmetric domains
w. G. Olafsson, Submitted (2020).

Coorbits for projective representations with an application to Bergman spaces
w. A. Darweesh and G. Olafsson, Monatsh. Math., Vol 189 (2019), no. 3, 385420.

Atomic decompositions of mixed norm Bergman spaces on tube type domains ,
Contemp. Math., 714 (2018), 7785.

Surjectivity of mean value operators on noncompact symmetric spaces,
w. F. Gonzalez and T. Kakehi in J. Funct. Anal. 272 (2017), no. 9, 36103646.

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), 205235

Multiwindow 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), 5569

Atomic decompositions of Besov spaces related to symmetric cones,
Contemporary Mathematics, Vol. 598 (2013), 97110

Coorbit description and atomic decomposition of Besov spaces,
w. A. Mayeli and G. Olafsson,
Numer. Funct. Anal. Optim., Vol. 33, Issue 79 (2012), 847871

Sampling in reproducing kernel Banach spaces on Lie groups,
Journal of Approximation Theory, Vol. 164 Issue 1 (2012), 179203

Coorbit Spaces for Dual Pairs,
w. G. Olafsson, Appl. Comp. Harm. Anal. Vol. 31 Issue 2 (2011), 303324

Examples of Coorbit Spaces for Dual Pairs
, w. G. Olafsson, Acta Appl. Math. 107 (2009), no. 13, 2548.

An uncertainty principle related to the Euclidean motion group
, w. H. Schlichtkrull, Math. Proc. R. Ir. Acad. 104A (2004), no. 2, 249252 (electronic)

The Uncertainty Principle for Operators Determined by Lie Groups
, J. Fourier Anal. Appl. 10 (2004), no. 5, 541544.
Refereed book chapters

Sampling in Euclidean and NonEuclidean 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).
Other research manuscripts

My Ph.D. dissertation titled
Function Spaces, Wavelets and Representation Theory
focuses on the interplay between representation theory
and the theory of Banach spaces of function or distributions.
In particular it suggests a generalization of the coorbit theory by
H.G. Feichtinger and K. Gröchenig.

My master's thesis titled
Uncertainty Principles
contains an overview of a few different uncertainty principles.
It also contains my first research contribution concerning
uncertainty principles derived from representations of Lie groups.
Uncertainty principles have had my interest since physics classes I took
as an undergraduate.
Books edited

Representation Theory and Harmonic Analysis on Symmetric Spaces,
Contemporary Mathematics, Volume 714 (2018).
Editors: Jens Christensen (main editor), Susanna Dann and Matthew Dawson

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

