Nonlinear wavelet approximation in anisotropic Besov spaces

Indiana University Mathematics Journal

Volumn 52, Issue 2, 2003, Pages 437-455

  Leisner, Christopher ^a  

^a FLORIDA ATLANTIC UNIVERSITY   (United States)

Author keywords

Anisotropic; B splines; Besov spaces; Interpolation spaces; Multiresolution; Nonlinear approximation; Wavelets

Indexed keywords

EID: 0038472370     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.2003.52.2224     Document Type: Article

References (21)

1. J. BERGH & J. LÖFSTRÖM Interpolation Spaces: an Introduction, Springer-Verlag, 1976.
2. M.Z. BERKOLAIKO & I. NOVIKOV, Unconditional bases in spaces of functions of anisotropic smoothness, Proc. Steklov Inst. Math. 3 (1994), 27-41.
3. RONALD A. DEVORE, BJÖRN JAWERTH & VASIL POPOV, Compression of wavelet decompositions, American Journal of Mathematics 114 (1992), 737-785.
4. RONALD A. DEVORE & G. LORENTZ Constructive Approximation, Springer-Verlag, Heidelberg, 1993.
5. RONALD A. DEVORE & V.A. POPOV, Interpolation of Besov spaces, Trans. Amer. Math. Soc. 305 (1988), 397-414.
6. _, Interpolation spaces and nonlinear approximation, In: Function Spaces and Applications (M. Cwikel, J. Peetre, Y. Sagher & H. Wallin, eds.), Volume 1302, Springer Lecture Notes in Math, 1988, 191-207.
7. D.L. DONOHO, CART and best-ortho-basis: a connection, Ann. Star. 25 (1997), 1870-1911.
8. WALTER FARKAS, Atomic and subatomic decompositions in anisotropic function spaces, Math. Nachr. 209 (2000), 83-113.
9. G. GARRIGÓS & A. TABACCO, Wavelet decompositions of anisotropic Besov spaces, preprint, Politecnico di Torino, 1999.
10. G. GARRIGÓS, R. HOCHMUTH & A. TABACCO, Wavelet characterization for anisotropic Besov spaces: case 0 < p < 1, Preprint Nr. A/14/00, Fachbereich Mathematik, Freie Universität Berlin, 2000.
11. R. HOCHMUTH, Wavelet bases in numerical analysis and restricted nonlinear approximation, Habilitation-Thesis, Freie Universität Berlin, 1999.
12. _, Anisotropic Besov spaces and wavelets, Proceedings of the International Wavelet Conference, Tanger, Institut National de Recherche en Informatique et en Automatique (Hrsg.), Tanger, 1998, 176-179.
13. A. KAMONT, Isomorphism of some anisotropic Besov and sequence spaces, Studia Math. 110 (1994), 169-189.
14. T.D. LONG & H. TRIEBEL, Equivalent norms and Shauder bases in anisotropic Besov spaces, Proceedings of the Royal Society of Edinburgh, 84A (1979), 177-183.
15. CHRISTOPHER LEISNER, Nonlinear wavelet approximation in anisotropic Besov spaces, Ph.D. Thesis, Purdue University, 2000.
16. M.H. NEUMANN & R. SACHS, Wavelet thresholding in anisotropic function classes and application to adaptive estimation of evolutionary spectra, Ann. Stat. 25 (1997), 38-76.
17. S.M. NIKOL'SKIJ, Approximation of Functions of Several Variables and Approximation Theorems, Springer-Verlag, 1975.
18. H. SCHMEISSER & H. TRIEBEL, Topics in Fourier Analysis and Function Spaces, John Wiley and Sons, 1987.
19. _, Anisotropic spaces I: Interpolation of abstract spaces and function spaces, Math. Nachr. 73 (1976), 107-123.
20. s type Math. Nachr. 89 (1979), 237-267.
21. V.N. TEMLYAKOV, Approximation of Periodic Functions, Nova Science Publishers Inc., New York, 1993.