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Shifted convolution of cusp-forms with $$\theta $$ θ -series [PDF]
Ramanujan Journal, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guangshi Lu, Jie Wu, Wenguang Zhai
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Convolutional PCA for Multiple Time Series
IEEE Signal Processing Letters, 2020We study a fundamental generalization of principal component analysis (PCA) that looks for a small set of common time series, i.e., principal components (PCs), whose filtered versions can explain most of the variances of multiple observed time series. This problem boils down to PCA in the frequency domain, in principle. But, frequency domain processing
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Shifted convolution of cusp-forms with θ-series
Abhandlungen Aus Dem Mathematischen Seminar Der Universitat Hamburg, 2011Taken 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
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The convolution sums of MacMahon’s q-series
The Ramanujan JournalIn his classical work on partitions and divisor functions, MacMahon introduced the two \(q\)-series \(A_k(q)\) and \(C_k(q)\), which have since been shown to be quasimodular forms and are closely linked to partition functions, modular forms, and infinite product identities.
Xia, Ernest X. W. +2 more
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Nonlinear convolution and fourier series coefficients estimate
2014 IEEE China Summit & International Conference on Signal and Information Processing (ChinaSIP), 2014In 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 ...
P Burrascano, Marco Ricci, Luca Senni
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Mapping Properties for Convolution Involving Hypergeometric Series
Ukrainian Mathematical Journal, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aouf, M. K. +2 more
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Weighted and Ergodic Theorems for Series of Differences of Convolutions
Journal of Fourier Analysis and Applications, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lorente, María, de la Torre, Alberto
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CONVOLUTIONS OF HECKE SERIES AND THEIR VALUES AT LATTICE POINTS
Mathematics of the USSR-Sbornik, 1977An algebraicity theorem is proved for the values of convolutions of Dirichlet series connected with modular forms of various weights at lattice points of the critical strip, -adic estimates of these values are obtained.Bibliography: 24 titles.
Manin, Yu. I., Panchishkin, A. A.
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Convolutional Neural Networks for Time Series Classification
2017This article concerns identifying objects generating signals from various sensors. Instead of using traditional hand-made time series features we feed the signals as input channels to a convolutional neural network. The network learned low- and high-level features from data.
Mariusz Zebik +3 more
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Time series convolution kernel estimation
AIP Conference Proceedings, 2018This paper focuses on descriptive analysis of time series using artificial neural networks. We used special type of neural networks architecture called convolutional neural networks to for estimation of convolutional kernels. These kernels were estimated from lookbehind window using Adam backpropagation algorithm and as such can be indicative of future
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