Dr. Kerstin Hesse
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PUBLICATIONS and PREPRINTS

APPROXIMATION THEORY

A. PUBLICATIONS in REFEREED JOURNALS

  1. Kerstin Hesse, Quoc Thong Le Gia: L_2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data. Journal of Computational and Applied Mathematics 408, (2022), 114118.
  2. Kerstin Hesse, Ian H. Sloan, Robert S. Womersley: Local RBF-based penalized least-squares approximation on the sphere with noisy scattered data. Journal of Computational and Applied Mathematics 382 (2021) 113061.
  3. Kerstin Hesse, Ian H. Sloan, Robert S. Womersley: Radial basis function approximation of noisy scattered data on the sphere. Numerische Mathematik, 137 (2017), 579-605.
  4. Kerstin Hesse, Robert S. Womersley: Numerical integration with polynomial exactness over a spherical cap. Advances in Computational Mathematics, 36 (2012), 451-483.
  5. Kerstin Hesse: Complexity of numerical integration over spherical caps in a Sobolev space setting. Journal of Complexity, 27 (2011), 383-403.
  6. Kerstin Hesse: The $s$-energy of spherical designs on $S^2$. Advances in Computational Mathematics, 30 (2009), 37-59.
  7. Kerstin Hesse, Paul Leopardi: The Coulomb energy of spherical designs on $S^2$. Advances in Computational Mathematics, 28 (2008), 331-354.
  8. Kerstin Hesse, Quoc Thong Le Gia: Local radial basis function approximation on the sphere. Bulletin of the Australian Mathematical Society, 77 (2008), 197-224.
  9. Kerstin Hesse, Hrushikesh N. Mhaskar, Ian H. Sloan: Quadrature in Besov spaces on the Euclidean sphere. Journal of Complexity, 23 (2007), 528-552.
  10. Kerstin Hesse, Frances Y. Kuo, Ian H. Sloan: A component-by-component approach to efficient numerical integration over products of spheres. Journal of Complexity, 23 (2007), 25-51.
  11. Johann S. Brauchart, Kerstin Hesse: Numerical integration over spheres of arbitrary dimension. Constructive Approximation, 25 (2007), 41-71.
  12. Kerstin Hesse: A lower bound for the worst-case cubature error on spheres of arbitrary dimension. Numerische Mathematik, 103 (2006), 413-433.
  13. Kerstin Hesse, Ian H. Sloan: Cubature over the sphere $S^2$ in Sobolev spaces of arbitrary order. Journal of Approximation Theory, 141 (2006), 118-133.
  14. Kerstin Hesse, Ian H. Sloan: Optimal lower bounds for cubature error on the sphere $S^2$. Journal of Complexity, 21 (2005), 790-803.
  15. Kerstin Hesse, Ian H. Sloan: Worst-case errors in a Sobolev space setting for cubature over the sphere $S^2$. Bulletin of the Australian Mathematical Society, 71 (2005), 81-105.
  16. Willi Freeden, Kerstin Hesse: On the multiscale solution of satellite problems by use of locally supported kernel functions corresponding to equidistributed data on spherical orbits. Studia Scientiarum Mathematicarum Hungarica, 39 (2002), 37-74.

B. OTHER PUBLICATIONS in non-refereed Journals

  1. Kerstin Hesse, Ian H. Sloan: High-order numerical integration on the sphere and extremal point systems. Journal of Computational Technologies, 9 (2004), 4-12 (invited paper, not refereed).

C. CHAPTERS in BOOKS

  1. Kerstin Hesse: RBF-based penalized least-squares approximation of noisy scattered data on the sphere. In: Multivariate Algorithms and Information-Based Complexity (eds.: F. J. Hickernell, P. Kritzer), De Gruyter, Berlin/Boston, 2020, pp. 33-42 (with peer review prozess).
  2. Kerstin Hesse, Ian H. Sloan, Robert S. Womersley: Numerical integration on the sphere. In: Handbook of Geomathematics (eds.: Willi Freeden, Zuhair Nashed and Thomas Sonar), Springer Verlag, 2010, pp. 1187-1220.
  3. Kerstin Hesse, Ian H. Sloan: Hyperinterpolation on the sphere. In: Frontiers in Interpolation and Approximation (Dedicated to the Memory of Ambikeshwar Sharma) (eds.: N. K. Govil, H. N. Mhaskar, Ram N. Mohapatra, Zuhair Nashed and J. Szabados), Chapman & Hall/CRC, 2006, pp. 213-248 (with peer review prozess).
  4. Kerstin Hesse, Ian H. Sloan: Optimal order integration on the sphere. In: Frontiers and Prospects of Contemporary Applied Mathematics, Series in Contemporary Applied Mathematics CAM 6 (eds.: Tatsien Li and Pingwen Zhang), Higher Education Press and World Scientific, 2005, pp. 59-70.

D. THESES (Diplom, Dr. rer. nat.)

  1. Kerstin Hesse: Domain Decomposition Methods in Multiscale Geopotential Determination from SST and SGG. Doctoral Thesis, Geomathematics Group, Department of Mathematics, University of Kaiserslautern, 2002. Published by Shaker Verlag, Aachen, 2003, 290 pages.
  2. Kerstin Hesse: Wachstumsverhalten von Lösungen der $\overline{\partial}$-Gleichung auf Pseudo-Siegel-Gebieten (Growth Behaviour of Solutions of the $\overline{\partial}$-Equation on Pseudo-Siegel-Domains). Diplomarbeit (“Diplom” Thesis), Mathematical Institute, University of Bonn, 1998, 118 pages. Download my Diplomarbeit.

E. In PREPARATION

  1. Kerstin Hesse, Ian H. Sloan, Robert S. Womersley: Smoothing approximation of noisy scattered data on the sphere with the hybrid approximation scheme.

F. PREPRINTS

  1. Willi Freeden, Kerstin Hesse: Spline modelling of geostrophic flow: theoretical and algorithmic aspects. Schriften zur Funktionalanalysis und Geomathematik No. 15, University of Kaiserslautern, December 2004, and Applied Mathematics Report AMR04/33, University of New South Wales, December 2004, 29 pages. This is a completely rewritten and improved version of preprint no. 3.
  2. Kerstin Hesse, Martin Gutting: Smoothing splines in multiscale geopotential determination from satellite data. Berichte der Arbeitsgruppe Technomathematik No. 255, University of Kaiserslautern, April 2003, 34 pages.
  3. Willi Freeden, Kerstin Hesse: Spline modelling of geostrophic flow: theoretical and algorithmic aspects. Berichte der Arbeitsgruppe Technomathematik No. 250, University of Kaiserslautern, August 2002, 45 pages.

MATHEMATICS EDUCATION
  1. Kerstin Hesse: Neugestaltung der “Höheren Mathematik A, B und C für Elektrotechniker” -- Nutzung der Lehrmaterialien durch Studierende. In: Hanse-Kolloquium zur Hochschuldidaktik der Mathematik 2015: Beiträge zum gleichnamigen Symposium am 13. & 14. November 2015 an der Universität zu Lübeck (Hochschulschriften zur Mathematik-Didaktik) (eds.: Walther Paravicini und Jörn Schnieder), WTM-Verlag, 2016, pp. 86-102.
  2. Kerstin Hesse: Online Tests for Evaluating Learning Success. Extended abstract for the khdm Conference 2015, 8 pages. (This extended abstract has been published online in a khdm report for the khdm Conference 2015.)