The convergence of operator with rapidly decreasing wavelet functions - Shamsah, Raghad S.; Ahmedov, Anvarjon A.; Kilicman, A.; Zainuddin, H. (Universiti Putra Malaysia, 2022)
The expansion of (2D) wavelet functions with respect to Lp(R2) space converging almost everywhere for 1 < p < 1 throughout the length of the Lebesgue set points of space functions is investigated in this research. The convergence is established by assuming somewavelet function minimal regularity ψ j1;j2;k1;k2 under the current description of the wavelet projection operator known as 2D Hard Sampling Operator. Note that the feature of fast decline in 2D is derived here. Another condition is used, for instance, the wavelet expansion’s boundedness under the Hard Sampling Operator. The bound (limit) is governed in magnitude with respect to the maximal equality of the Hardy-Littlewood maximal operator. Some ideas presented in this work to find a new method to prove the convergence theory for new type of conditional wavelet operator. Propose some conditions for wavelets functions and there expansion can support the operator to be convergence. It also perform a comparison with the identity convergent operator is our method for achieving this convergence.