In this paper, we deal with the convolution series that are a far reaching generalization of conventional power and fractional exponents including Mittag-Leffler type functions. Special attention is given to most interesting case generated by Sonine kernels. first formulate prove second fundamental theorem for general integrals $n$-fold sequential derivatives both Riemann-Liouville Caputo types...

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 a locally compact semigroup. On locally compact quantum groups we obtain a bijective cor...

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...