Detail A smoothness property of wavelet paraproducts Bibliografi Author: Canning, Eric Patrick ; Bennett, Andrew G. (Advisor) Topik: MATHEMATICS Bahasa: (EN )    ISBN: 0-599-44304-9     Penerbit: KANSAS STATE UNIVERSITY     Tahun Terbit: 1999     Jenis: Theses - Dissertation Fulltext: 9942660.pdf (0.0B; 0 download) Abstract In 1981, Jean-Michel Bony introduced paraproducts. Paraproducts radially cut the supports of the Fourier transforms of two functions, f and g, into dyadic intervals, multiply the pieces together, and sum up these parts to recover f · g. The reason for doing this is that paraproducts allow us to isolate the parts of f · g that are of different degrees of smoothness. Bony uses paraproducts to prove theorems about the smoothness of solutions of nonlinear partial differential equations. These “traditional” paraproducts are constructed using the Fourier transform. In this thesis, we define the “wavelet” paraproduct, a paraproduct that is built using the wavelet transform rather than the Fourier transform. We prove a smoothness result for wavelet paraproducts that is the same as the result for traditional paraproducts, though the proof is quite different. The proof involves an almost-orthogonality argument and makes use of theorems about the boundedness of Calderón-Zygmund operators on certain function spaces. Opini Anda Klik untuk menuliskan opini Anda tentang koleksi ini! Lihat Sejarah Pengadaan  Konversi Metadata   Kembali

Copyright © 2006, 2007 Unika Atma Jaya, all rights reserved