Optical convolution kernel based on the volatile-modulation-compatible photonic memory: (a) Schematic architecture of a 4×4 OCK. The inset is the discrete device of OCK.

The convolution of two φ-convex functions is estimated by means of an inequality of Hadamard type. The sharpness of this inequality is discussed. As consequence, few inequalities for the convolution ...

Observing that the history term is a convolution of the history of f and a regular kernel, we derive a multipole approximation to the Laplace transform of the kernel. This enables the history term to ...