Jens Gerlach Christensen
Associate Professor
Department of Mathematics
Colgate University
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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
  • Time-frequency analysis
  • Representation theory
  • Uncertainty principles
  • Frames and wavelets
  • Reproducing kernel Banach spaces
  • Sampling theory
  • Mean value operators and Radon transforms

Publications

Articles

  1. New atomic decompositions of Bergman spaces on bounded symmetric domains w. G. Olafsson, Submitted (2020).
  2. Coorbits for projective representations with an application to Bergman spaces w. A. Darweesh and G. Olafsson, Monatsh. Math., Vol 189 (2019), no. 3, 385-420.
  3. Atomic decompositions of mixed norm Bergman spaces on tube type domains , Contemp. Math., 714 (2018), 77-85.
  4. 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.
  5. 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
  6. 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
  7. Atomic decompositions of Besov spaces related to symmetric cones, Contemporary Mathematics, Vol. 598 (2013), 97-110
  8. 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
  9. Sampling in reproducing kernel Banach spaces on Lie groups, Journal of Approximation Theory, Vol. 164 Issue 1 (2012), 179-203
  10. Coorbit Spaces for Dual Pairs, w. G. Olafsson, Appl. Comp. Harm. Anal. Vol. 31 Issue 2 (2011), 303-324
  11. Examples of Coorbit Spaces for Dual Pairs , w. G. Olafsson, Acta Appl. Math. 107 (2009), no. 1-3, 25--48.
  12. An uncertainty principle related to the Euclidean motion group , w. H. Schlichtkrull, Math. Proc. R. Ir. Acad. 104A (2004), no. 2, 249--252 (electronic)
  13. The Uncertainty Principle for Operators Determined by Lie Groups , J. Fourier Anal. Appl. 10 (2004), no. 5, 541--544.

Refereed book chapters

  1. 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).
  2. 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

  1. Representation Theory and Harmonic Analysis on Symmetric Spaces, Contemporary Mathematics, Volume 714 (2018). Editors: Jens Christensen (main editor), Susanna Dann and Matthew Dawson
  2. 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
  3. 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