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Near-field-free super-potential FFT method for the three-dimensional free-space Poisson equation

Exl L, Schaffer S.
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Hadamard–Bergman Convolution Operators

Complex Analysis and Operator Theory, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Karapetyants, Alexey, Samko, Stefan
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Hyperbolic Convolution Operators

Canadian Journal of Mathematics, 1965
Hyperbolic differential operators with constant coefficients introduced and studied systematically by Gårding (4), were characterized by the existence of the fundamental solution with some cone condition, according to Hörmander (6). Recently Ehrenpreis, extending the notion of hyperbolicity due to Gårding, has defined hyperbolic operators for ...
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Sums of Convolution Operators

SIAM Journal on Mathematical Analysis, 1972
Let $\Omega $ be an open set in $R_n $ and let $\mathcal{E}(\Omega )$ denote the space of infinitely differentiable functions on $\Omega $. Necessary and sufficient conditions are exhibited for a family $\{ \Omega _i \} _{i = 1}^N $ of open sets in $R_n$ and a family $\{ S_i \} _{i = 1}^N \subset \mathcal{E}'(R_n )$ in order that the convolution ...
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Integral convolution operators

Mathematical Notes of the Academy of Sciences of the USSR, 1985
Let \(E_ 1,E_ 2\) and \(E_ 3\) be symmetric function spaces on an interval [0,a]. The following problem is under investigation: under which conditions is the convolution operator continuous from \(E_ 1\times E_ 2\) into \(E_ 3?\) The author gives some sufficient conditions for the continuity in terms of the Boyd indices \(\alpha_ E\) and \(\beta_ E ...
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On integral convolution operators

Mathematical Notes, 1999
We study integral convolutions defined on functions ofn variables in symmetric spaces and obtain new additive estimates for the mean value of the nonincreasing permutation(K*f)**(t) of the absolute value of the integral convolution on the interval [0,t] for anyt>0.
B. I. Peleshenko, V. A. Katan
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Convolution operators

1997
Abstract This chapter is, like Chapter 3, slanted towards practical applications in systems identiflcation—this time using input/output measurements rather than transfer function measurements. The question of input design is an important one in this problem and its solution draws heavily upon ideas from Galois theory and classical ...
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Hypercyclic and Chaotic Convolution Operators

Journal of the London Mathematical Society, 2000
Every convolution operator on a space of ultradifferentiable functions of Beurling or Roumieu type and on the corresponding space of ultradistributions is hypercyclic and chaotic (i.e., it is transitive and has a dense set of periodic points) when it is not a multiple of the identity.
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Entropy of a Convolution Operator

Open Systems & Information Dynamics, 2004
The concept of the entropy of a doubly stochastic operator was introduced in 1999 by Ghys, Langevin, and Walczak. The idea was developed further by Kamiński and de Sam Lazaro, who also conjectured that the entropy of a convolution operator determined by a probability measure on a compact abelian group is equal to zero.
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Dunkl operators as convolutions

Doklady Mathematics, 2008
Let \(\varphi \) be an analytic function of entire type with \(\varphi (0)=0\) and define the operator \(A\) on \(H(\mathbb C)\), the space of entire functions, by \[ A(f)=\frac1z\sum_{k=0}^\infty \varphi (k)c_kz^k,\quad f(z)=\sum_{k=1}^\infty c_kz^k\in H(\mathbb C).
Napalkov, V. V., Napalkov, V. V. jun.
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