Results 251 to 260 of about 4,390,707 (282)

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.
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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
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Series concatenation of 2D convolutional codes

2015 IEEE 9th International Workshop on Multidimensional (nD) Systems (nDS), 2015
In this paper we study two-dimensional (2D) con-volutional codes which are obtained from series concatenation of two 2D convolutional codes. In this preliminary work we confine ourselves to dealing with finite-support 2D convolutional codes and make use of the so-called Fornasini-Marchesini input-state-output (ISO) model representations. In particular,
Joan-Josep Climent, Diego Napp, Raquel Pinto, Rita Simões   +3 more
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Convolutional PCA for Multiple Time Series

IEEE Signal Processing Letters, 2020
We 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, 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

The convolution sums of MacMahon’s q-series

The Ramanujan Journal
In 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., Fan, Yan, Yao, Olivia X. M.   +2 more
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Weighted and Ergodic Theorems for Series of Differences of Convolutions

Journal of Fourier Analysis and Applications, 2008
zbMATH 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, 1977
An 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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Mapping Properties for Convolution Involving Hypergeometric Series

Ukrainian Mathematical Journal, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aouf, M. K., Mostafa, A. O., Zayed, H. M.   +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), 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 ...
BURRASCANO, Pietro, RICCI, MARCO, BATTAGLINI, LUIGI, SENNI, Luca   +3 more
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