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Journal of Function Spaces and Applications, 2010 H1(R) is a Banach algebra which has better mapping properties under singular integrals than L1(R) . We show that its approximate identity sequences are unbounded by constructing one unbounded approximate identity sequence {vn}.
R. L. Johnson, C. R. Warner
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Multi-Dimensional Definition of Convolution
Современные информационные технологии и IT-образование, 2021 Convolution is an indispensable operation for solving problems from a variety of subject areas: machine learning problems, data analysis, signal processing, image processing filters.
Evgeniy Goncharov
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Lie Group Algebra Convolutional Filters [PDF]
IEEE Transactions on Signal Processing, 2023 In this paper we propose a framework to leverage Lie group symmetries on arbitrary spaces exploiting algebraic signal processing (ASP). We show that traditional group convolutions are one particular instantiation of a more general Lie group algebra ...
Harshat Kumar +2 more
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GALA: Greedy ComputAtion for Linear Algebra in Privacy-Preserved Neural Networks [PDF]
Network and Distributed System Security Symposium, 2021 Machine Learning as a Service (MLaaS) is enabling a wide range of smart applications on end devices. However, privacy-preserved computation is still expensive.
Qiao Zhang, Chunsheng Xin, Hongyi Wu
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Современные информационные технологии и IT-образование, 2022 Multidimensional matrix algebra is a successful data model for problems from a variety of subject areas. Many authors have described hardware and software complexes that implement the algebra of multidimensional matrices in its entirety or parallel ...
Evgeniy I. Goncharov
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Convolution algebras for topological groupoids with locally compact fibres [PDF]
Opuscula Mathematica, 2011 The aim of this paper is to introduce various convolution algebras associated with a topological groupoid with locally compact fibres. Instead of working with continuous functions on \(G\), we consider functions having a uniformly continuity property on ...
Mădălina Roxana Buneci
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Renormalization group-like proof of the universality of the Tutte polynomial for matroids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 In this paper we give a new proof of the universality of the Tutte polynomial for matroids. This proof uses appropriate characters of Hopf algebra of matroids, algebra introduced by Schmitt (1994). We show that these Hopf algebra characters are solutions
G. Duchamp +3 more
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Speed of convergence of complementary probabilities on finite group
Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika, 2021 Let function P be a probability on a finite group G, i.e. $P(g)\geq0\ $ $(g\in G),\ \sum\limits_{g}P(g)=1$ (we write $\sum\limits_{g}$ instead of $\sum\limits_{g\in G})$.
Alexander Vyshnevetskiy
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Catoids and modal convolution algebras
Algebra Universalis, 2023 We show how modal quantales arise as convolution algebras $$Q^X$$ Q X of functions from catoids X , multisemigroups equipped with source and target maps, into modal quantales value or weight quantales Q .
Uli Fahrenberg +3 more
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$\mathcal{E}'$ as an algebra by multiplicative convolution [PDF]
Functiones et Approximatio Commentarii Mathematici, 2015 We study the algebra $\mathscr{E}'(\mathbb{R}^d)$ equipped with the multiplication $(T\star S)(f)=T_x(S_y(f(xy))$ where $xy=(x_1y_1,\dots,x_dy_d)$.
D. Vogt
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