Atomic functions are widely applied in interpolation, boundary-value problems, digital signal and image processing. In the report convolutions of atomic functions are discussed. It is shown that convolutions of atomic functions with same scale parameter are atomic functions too. Basing on this approach new family of atomic functions cha,n is presented. Iterative algorithms for computation of new functions are constructed.
Atomic functions present an effective mathematical apparatus for interpolation of functions. Given function is represented as a sum of scaled shifts of compactly supported atomic function. Fundamental property of such interpolation is that derivatives of given function are simultaneously interpolated with corresponding derivatives of interpolation. This property allows application of atomic function to numerical solution of differential equations.
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