Wavelets on manifolds: An optimized construction

Mathematics of Computation

Volumn 75, Issue 255, 2006, Pages 1319-1349

  Kunoth, Angela ^a   Sahner, Jan ^b  

^a UNIVERSITY OF BONN   (Germany)

^b ZUSE INSTITUTE BERLIN   (Germany)

Author keywords

2 sphere; Biorthogonal wavelets; Extension operators; Optimized Hestenes extension; Topological isomorphisms; Trace dependent operators; Wavelets on manifolds

Indexed keywords

EID: 33746341474     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-06-01828-X     Document Type: Article

References (15)

1. [A] R. Adams, Sobolev Spaces, Academic Press, 1975. MR0450957 (56 #9247)
2. [B] D. Bertsekas, Nonlinear Programming, Athena Scientific, 1999.
3. [Bo] C. de Boor, A Practical Guide to Splines, Applied Mathematical Sciences 27, Springer, 2003. MR0507062 (80a:65027)
4. ∞ manifolds: Part I and II, Studia Mathematica, 1983, 1-58 and 95-136. MR0728195 (85f:46060a) and MR0730015 (85f:46060b)
5. [CTU] C. Canuto, A. Tabacco, K. Urban, The wavelet element method, part I: Construction and analysis, Appl. Comput. Harm. Anal. 6, 1999, 1-52. MR1664902 (99k:42055)
6. [DKU] W. Dahmen, A. Kunoth, K. Urban, Biorthogonal spline wavelets on the interval-Stability and moment conditions, Appl. Comput. Harmon. Anal. 6, No.2, 1999, 132-196. MR1676771 (99m:42046)
7. [DS] W. Dahmen, R. Schneider, Wavelets on manifolds I: Construction and domain decomposition, SIAM J. Math. Anal. 31, No. 1, 1999, 184-230. MR1742299 (2000k:65242)
8. [DS1] W. Dahmen, R. Schneider, Composite wavelet bases for operator equations, Math. Comp. 68, 1999, 1533-1567. MR1648379 (99m:65122)
9. [DS2] W. Dahmen, R. Schneider, Wavelets with complementary boundary conditions - function spaces on the cube, Results in Mathematics 34, 1998, 255-293. MR1652724 (99h:42057)
10. [DSt] W. Dahmen, R. Stevenson, Element-by-element construction of wavelets satisfying stability and moment conditions, SIAM J. Numer. Anal. 37, No. 1, 1999, 319-352. MR1742747 (2001c:65144)
11. [H] M. R. Hestenes, Extension of the range of a differentiable function, Duke Math. J. 8, 1941, 183-192. MR0003434 (2,219c)
12. [Ha] H. Harbrecht, Wavelet Galerkin Schemes for the Boundary Element Method in Three Dimensions, Dissertation, Technische Universität Chemnitz, 2001.
13. [IGPM] A. Barinka, T. Bartsch, K. Urban, J. Vorloeper, The Multilevel Library, Institut für Geometrie und Praktische Mathematik, RWTH Aachen, 2001.
14. [KS] A. Kunoth, J. Sahner, Wavelets on manifolds: An optimized construction (extended version), SFB 611 Preprint #163, Universität Bonn, July 2004, revised, April 2005, available at http://www.ins.uni-bonn.de/~kunoth/ papers/papers.html
15. [S] J. Sahner, On the Optimized Construction of Wavelets on Manifolds, Diploma Thesis (in English), Universität Bonn, September 2003.