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Shifted convolution of cusp-forms with θ-series

Abhandlungen Aus Dem Mathematischen Seminar Der Universitat Hamburg, 2011
Taken from the abstract of the article: The author generalizes the classical Voronoi formula for \[ r_l(n) = \#\{(n_1,\ldots,n_l) \in \mathbb{Z}^l, n_1^2+\cdots+n_l^2 = n \}, \] and as an application, a sharp bound for the shifted convolution sum convolving Fourier coefficients of holomorphic cusp forms with those of theta series is obtained.
Wenzhi Luo
exaly   +3 more sources

Nonlinear convolution and fourier series coefficients estimate

2014 IEEE China Summit & International Conference on Signal and Information Processing (ChinaSIP), 2014
In the present the paper an original description of the procedure for the modeling of nonlinear systems based on the socalled non linear convolution approach [1, 2, 3] is reported. This approach relies on the modeling of a nonlinear system by means of the linear convolution and we show how, in the case of memoryless nonlinear systems, the method is ...
Luca Senni   +2 more
exaly   +3 more sources

A Convolution Structure for Jacobi Series

American Journal of Mathematics, 1969
Gangolli [6] discovered this convolution structure for special values of ac and J3 namely /3= 1/2, a = (n -1)/2; 3=0, ac n; and /3=1, a-2n + 1; 1 G= 3, c = 7. n here is a non-negative integer. Let P (a,0) (x) be the Jacobi polynomial of degree n, order (2,/) defined by P(?()are orthogonal onl (-1, 1) writh resplect tO ( 1 0x)at(1 ?
Askey, R., Wainger, S.
openaire   +2 more sources

Convolutional Neural Networks with Dynamic Convolution for Time Series Classification

2021
Due to its prominent applications, time series classification is one of the most important fields of machine learning. Although there are various approaches for time series classification, dynamic time warping (DTW) is generally considered to be a well-suited distance measure for time series.
Krisztián Búza, Margit Antal
openaire   +2 more sources

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