Almost Everywhere Convergence of Soho Wavelet Expansions With Spherical Wavelet Summation Method

The Convergence of Operator With Rapidly Decreasing Wavelet Functions

“…convergent). This work is completing the ideas of the work of the [11] by verifying two dimensional rapidly decreasing property for wavelet function which allows to achieve the almost everywhere convergence. Properties of the two-dimensional version of the Hard Sampling operator are obtained and applied to establish the proof of the almost everywhere convergence of the wavelet expansions of the rapidly decreasing functions.…”

“…In a different work, [13] used a prolate spheroidal wavelet to examine the pointwise convergence of wavelet expansions of L 2 (R) functions. In addition, [12]and [11] looked at how L P functions defined on the S 2 and R 2 domains converge. By utilizing a spherical multi-resolution analysis on S 2 surface functions, [11] elucidated the pointwise behavior of spherical wavelet expansion with respect to the spherical wavelet projection operator.…”

“…In addition, [12]and [11] looked at how L P functions defined on the S 2 and R 2 domains converge. By utilizing a spherical multi-resolution analysis on S 2 surface functions, [11] elucidated the pointwise behavior of spherical wavelet expansion with respect to the spherical wavelet projection operator. Hence, redefining the projection operator into 2D wavelet projections operators and expanding the 0-regular wavelet function with two scaling and shifting parameters, [12] enhanced Tao's work.…”

A Bounded Maximal Function Operator and Its Acting on <img src=image/13425593_01.gif> Functions

“…Many researchers dealt with pointwise convergence topics in which wavelet expansions are defined on real lines or space. On the other hand, Raghad et al [17] employed a spherical multiresolution analysis on S 2 surface by discussing the pointwise convergence of SOHO wavelet expansions. To the best of the author's knowledge, this study is the first one to generalize the findings of Raghad et al [17] by discussing the pointwise convergence of scaling wavelet expansions under Scaling Wavelet Projections Operators defined on S 2 surfaces.…”

“…On the other hand, Raghad et al [17] employed a spherical multiresolution analysis on S 2 surface by discussing the pointwise convergence of SOHO wavelet expansions. To the best of the author's knowledge, this study is the first one to generalize the findings of Raghad et al [17] by discussing the pointwise convergence of scaling wavelet expansions under Scaling Wavelet Projections Operators defined on S 2 surfaces. We utilize L p functions and expand them on the unit sphere, referring to the functions represented by wavelet basis functions defined on S 2 .…”