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ARKCoS (Accelerated radial kernel convolution on the sphere) efficiently convolves pixelated maps on the sphere with radially symmetric kernels with compact support. It performs the convolution along isolatitude rings in Fourier space and integrates in longitudinal direction in pixel space. The computational costs scale linearly with the kernel support, making the method most beneficial for convolution with compact kernels. Typical applications include CMB beam smoothing, symmetric wavelet analyses, and point-source filtering operations. The software is written in C++/CUDA and provides two independent code paths to do the necessary computation either on conventional hardware (CPUs), or on graphics processing units (GPUs).