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Integral convolution operators
Mathematical Notes of the Academy of Sciences of the USSR, 1985Let \(E_ 1,E_ 2\) 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, 1999We 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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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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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, 2000Every 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, 2004The 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, 2008Let \(\varphi \) 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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A right inverse operator of the convolution operator
Ukrainian Mathematical Journal, 1991zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Convolutions of Generating Operators
1994We considered convolutions of the generalized H-transforms in Chapter 11. The main property of these convolutions is the following {fy205-1} where (H a f)(x) is the generalized H-transform with the power weight (11.1). It follows from this relation that the H-convolution (f * a )(x) is connected with some integral transform and this connection is ...
Semen B. Yakubovich, Yurii F. Luchko
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Approximation by convolution operators
Analysis Mathematica, 1982слЕДУь п. к. сИккЕМА, Мы ИсслЕДУЕМ АппРОксИМ АцИОННыЕ сВОИстВА ОпЕРАтОРОВ $$u_\varrho ^\beta (f,x) = \frac{1}{{\beta _\varrho }}\int\limits_{ - \infty }^\infty {f(x - t)\beta ^\varrho (t) dt(\varrho \to \infty ).} $$
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