Positive definite functions of non monoton variogram to define the spatial dependency of correlogram

The covariance function that forms a variogram is an important measurement for spatial dependence and as a linear kriging interpolation tool. The covariance function requires a definite positive guarantee, this means that not all functions can be used. Therefore, this research explores the correlogram and nonmonoton variogram functions and shows it analytically using the Fourier Transform (Bochner’s theorem). In addition, a simple approach is used to determine definite positivity by paying attention to boundaries. Suppose that C : Rd → R is positive definite if it bounded to exponential which is positive definit. Research shows that Nonmonoton Bessel functions that have Exponential bound are positive definite. Multiplication operations of two covariance functions, C1 and C2 in measured spaces indicate that definite positive properties are fulfilled.