Wavelet Bases for Microlocal Filtering and the Sampling Theorem in L_p(Rⁿ)∗

An orthonormal wavelet basis in L 2 used for microlocal filters, which decompose signals into microlocal contents, is shown to be a "stepwise" unconditional basis in L p (1 < p < X ). Other related spaces are also treated. As part of the proof, an elementary proof of the L p version of the sampling theorem with unconditional convergence is given. Finally, an application is given to the expression of some distributions as sums of boundary values of holomorphic functions.

Keywords:

• Orthonormal Wavelets
• Microlocal Filtering
• Sampling Theorem
• L p Space
• Sobolev Space
• Unconditional Convergence