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TVMVP (version 1.0.5)

two_fold_convolution_kernel: Two-Fold Convolution Kernel Function

Description

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 \([-2, 2]\).

Usage

two_fold_convolution_kernel(u, kernel_func)

Value

A numeric vector of two-fold convolution kernel values corresponding to each input u.

Arguments

u

A numeric vector of points at which the two-fold convolution kernel is evaluated.

kernel_func

A function representing the kernel to be convolved.

Details

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.