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Convolutional kernel function algebra [PDF]
Frontiers in Computer Science, 2022 Many systems for image manipulation, signal analysis, machine learning, and scientific computing make use of discrete convolutional filters that are known before computation begins.
Edward Stow, Paul H. J. Kelly
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The Kernel of a Block of a Group Algebra [PDF]
Proceedings of the American Mathematical Society, 1973 Avoiding the theory of characters of finite groups and group algebras over fields of characteristic zero a ring theoretical proof is given for R. Brauer’s theorem which asserts that the (modular) kernel of a block of a group algebra FG of a finite group over a field F of characteristic p > 0 p > 0 is a p ...
Gerhard O. Michler
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Kernel L-Ideals and L-Congruence on a Subclass of Ockham Algebras [PDF]
Journal of Mathematics, 2022 In this paper, we study L-congruences and their kernel in a subclass Kn,0 of the variety of Ockham algebras A. We prove that the class of kernel L-ideals of an Ockham algebra forms a complete Heyting algebra.
Teferi Getachew Alemayehu +2 more
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Algebraicity of the Bergman Kernel
Mathematische Annalen, 2020 Our main result introduces a new way to characterize two-dimensional finite ball quotients by algebraicity of their Bergman kernels. This characterization is particular to dimension two and fails in higher dimensions, as is illustrated by a counterexample in dimension three constructed in this paper.
Peter Ebenfelt, Ming Xiao, Hang Xu
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Analytic Group Kernels and Lie Algebra Kernels [PDF]
Transactions of the American Mathematical Society, 1960 84 p. ; Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1955.
R. A. Macauley
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On the extension of positive definite kernels to topological algebras [PDF]
Journal of Mathematical Physics, 2020 We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras and describe their associated reproducing kernel spaces. The case of entire functions is of special interest, and we give a precise meaning to some power series expansions of analytic functions that appears in many algebras.
Daniel Alpay, Ismael L. Paiva
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Multiresolution kernel matrix algebra [PDF]
Numerische MathematikAbstractWe propose a sparse algebra for samplet compressed kernel matrices to enable efficient scattered data analysis. We show that the compression of kernel matrices by means of samplets produces optimally sparse matrices in a certain S-format. The compression can be performed in cost and memory that scale essentially linearly with the number of data
H. Harbrecht +3 more
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The convolution algebra of Schwarz kernels on a singular foliation [PDF]
Journal of Operator Theory, 2019 Motivated by the study of H\"ormander's sums-of-squares operators and their generalizations, we define the convolution algebra of transverse distributions associated to a singular foliation. We prove that this algebra is represented as continuous linear operators on the spaces of smooth functions and generalized functions on the underlying manifold ...
Iakovos Androulidakis +2 more
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The inner kernel theorem for a certain Segal algebra [PDF]
Monatshefte für Mathematik, 2022 AbstractThe Segal algebra$${\mathbf{S}}_{0}(G)$$S0(G)is well defined for arbitrary locally compact Abelian Hausdorff (LCA) groupsG. It is a Banach space that exhibits a kernel theorem similar to the well-known Schwartz kernel theorem. Specifically, we call this characterization of the continuous linear operators from$${\mathbf{S}}_{0}(G_1)$$S0(G1)to$${\
Hans G. Feichtinger, Mads S. Jakobsen
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Kernel algebras and generalized Fourier-Mukai transforms
Journal of Noncommutative Geometry, 2008 We introduce and study kernel algebras , i.e., algebras in the category of sheaves on a square of a scheme, where the latter category is equipped with a monoidal structure via a natural convolution operation. We show that many interesting categories, such as D-modules, equivariant sheaves and their twisted versions,
Alexander Polishchuk
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