A NEW CLASS OF UNBALANCED HAAR WAVELETS THAT FORM AN UNCONDITIONAL BASIS FOR Lp ON GENERAL MEASURE SPACES
نویسنده
چکیده
Given a complete separable nite measure space (X; ; ) and nested partitions of X, we construct unbalanced Haar-like wavelets on X that form an unconditional basis for Lp(X; ; ) where 1 < p <1. Our construction and proofs build upon ideas of Burkholder and Mitrea. We show that if (X; ; ) is not purely atomic, then the unconditional basis constant of our basis is (max(p; q) 1). We derive a fast algorithm to compute the coe cients.
منابع مشابه
The Haar wavelets and the Haar scaling function in weighted L p spaces with A dy , mp weights
The new class of weights called A p weights is introduced. We prove that a characterization and an unconditional basis of the weighted Lp space Lp(Rn,w(x)dx) with w ∈ A p (1 < p < ∞) are given by the Haar wavelets and the Haar scaling function. As an application of these results, we establish a greedy basis by using the Haar wavelets and the Haar scaling function again.
متن کاملSummary of Research Accomplishments
1. Wavelets. One of my early accomplishments was the construction of wavelets on hyper-surfaces, extending the two-dimensional work in Coifman, Jones, Semmes (J. of Amer. Math. Soc., 1989), in a desirable fashion. This answered a question raised by G. David (Springer LNM, 1991, p. 75) and was used to provide a new proof of the fundamental result of Coifman, McIntosh, Meyer (Annals of Math., 198...
متن کاملThe Lifting Scheme: A Construction Of Second Generation Wavelets
Improved technique for design of perfect reconstruction r QMF banks with lossless polyphase matrices. Energy moments in time and frequency for two-scale diierence equation solutions and wavelets. SIAM 33 70] S. G. Mallat. Multifrequency channel decompositions of images and wavelet models. 89] W. Sweldens. The lifting scheme: A custom-design construction of biorthogonal wavelets. A new class of ...
متن کاملSolving infinite horizon optimal control problems of nonlinear interconnected large-scale dynamic systems via a Haar wavelet collocation scheme
We consider an approximation scheme using Haar wavelets for solving a class of infinite horizon optimal control problems (OCP's) of nonlinear interconnected large-scale dynamic systems. A computational method based on Haar wavelets in the time-domain is proposed for solving the optimal control problem. Haar wavelets integral operational matrix and direct collocation method are utilized to find ...
متن کاملAPPLICATION OF HAAR WAVELETS IN SOLVING NONLINEAR FRACTIONAL FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS
A novel and eective method based on Haar wavelets and Block Pulse Functions(BPFs) is proposed to solve nonlinear Fredholm integro-dierential equations of fractional order.The operational matrix of Haar wavelets via BPFs is derived and together with Haar waveletoperational matrix of fractional integration are used to transform the mentioned equation to asystem of algebraic equations. Our new met...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1995