Translation and convolution associated with discrete wavelet transform are investigated using properties of Calderón-Zygmund operator and Riesz fractional integral operator. Dual convolution is also studied. The wavelet convolution is applied to approximate functions belonging to certain p L-spaces.

Convolutional neural networks (CNNs) are a popular and highly performant choice for pixel-wise dense prediction or generation. One of the commonly required components in such CNNs is a way to increase the resolution of the network’s input. The lower resolution inputs can be, for example, low-dimensional noise vectors in image generation [7] or low resolution (LR) feature maps for network vis...

—We introduce the boolean convolution for probability measures on the unit circle. Roughly speaking, it describes the distribution of the product of two boolean independent unitary random variables. We find an analogue of the characteristic function and determine all infinitely divisible probability measures on the unit circle for the boolean convolution. Résumé (Convolution booléenne de probab...

Convolution semigroups of states on a quantum group form the natural noncommutative analogue of convolution semigroups of probability measures on a locally compact group. Here we initiate a theory of weakly continuous convolution semigroups of functionals on a C∗bialgebra, the noncommutative counterpart of locally compact semigroup. On locally compact quantum groups we obtain a bijective corres...

The Special Affine Fourier Transform or the SAFT generalizes a number of well known unitary transformations as well as signal processing and optics related mathematical operations. Unlike the Fourier transform, the SAFT does not work well with the standard convolution operation. Recently, Q. Xiang and K. Y. Qin introduced a new convolution operation that is more suitable for the SAFT and by whi...

Given two planar curves, their convolution curve is defined as the set of all vector sums generated by all pairs of curve points which have the same curve normal direction. The Minkowski sum of two planar objects is closely related to the convolution curve of the two object boundary curves. That is, the convolution curve is a superset of the Minkowski sum boundary. By eliminating all redundant ...

A notion of convolution is presented in the context of formal power series together with lifting constructions characterising algebras of such series, which usually are quantales. A number of examples underpin the universality of these constructions, the most prominent ones being separation logics, where convolution is separating conjunction in an assertion quantale; interval logics, where conv...

Given two planar curves, their convolution curve is defined as the set of all vector sums generated by all pairs of curve points which have the same curve normal direction. The Minkowski sum of two planar objects is closely related to the convolution curve of the two object boundary curves. That is, the convolution curve is a superset of the Minkowski sum boundary. By eliminating all redundant ...