Some Research About MCM Series

Determination of jumps for functions is an important part of detection of singularrities of a function. Now,many authors are interested in this area.Recent-ly, X. L. Shi and L.Hu published the method of concentration factors for de-termination of jumps of functions via MCM Conjugate Wavelets.So,it is easy for us to use MCM derivative series to replace MCM Conjugate Wavelets which can conclude the jump of the functions. When we use MCM Conjugate Wavelets to conclude the jumps of the Non-periodic function we introduce the Hilbert Transform of the function.It is known that Hilbert transform itself contains the function at the point xi function value of the difference between left and right.In the second chapter by Poisson and Gaussian kernel Hilbert nuclear transformation in order to effect the function of the jump in the dis-continuous point value.