This function computes the two-fold convolution of a given kernel function with itself. The convolution is evaluated over a range of inputs \(u\) and is set to zero outside the interval \([-2, 2]\).
two_fold_convolution_kernel(u, kernel_func)A numeric vector of two-fold convolution kernel values corresponding to each input u.
A numeric vector of points at which the two-fold convolution kernel is evaluated.
A function representing the kernel to be convolved.
The two-fold convolution kernel is defined as:
$$
K^{(2)}(u) = \int_{-1}^{1} K(v) \cdot K(u - v) \, dv
$$
where \(K\) is the original kernel function. The function evaluates this convolution for each
input u within the interval \([-2, 2]\) and sets it to zero outside this range.