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ON FUNDAMENTAL OPERATIONS FOR MULTIMODULAR FUNCTIONS
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Moriguchi, Satoko, Murota, Kazuo
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Abstractions of sequences, functions and operators
Abstract We present theoretical and practical results on the order theory of lattices of functions, focusing on Galois connections that abstract (sets of) functions – a topic known as higher-order abstract interpretation .
Rustenholz, Louis +2 more
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Operators on function spaces [PDF]
Brooks, James K., Lewis, Paul W.
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Functions which operate on characteristic functions [PDF]
Konheim, Alan G., Weiss, Benjamin
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ON THE OPERATIONAL CALCULUS WITH DIFFERENTIABLE FUNCTIONS [PDF]
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Operator Hypergeometric Functions
Journal of Mathematical Sciences, 2023The paper deals with differential equations \[ Du=Au\tag{1} \] with a differential operator \(D\) and unbounded operator coefficients \(A\). If the case when the Cauchy problem for equation (1) is uniformly well-posed then its solution can be represented via transformation operator.
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Classes of Operator-Smooth Functions - II. Operator-Differentiable Functions
Integral Equations and Operator Theory, 2004The paper continues a study of operator-smooth functions of a real variable started in [Proc. Edinb. Math. Soc., II. Ser. 48, 151--173 (2005; Zbl 1065.47010)] and deals with the spaces of Gâteaux and Fréchet operator differentiable functions. The authors introduce the notion of Gâteaux and Fréchet \(J\)-differentiable functions for symmetrically normed
Kissin, E., Shulman, V. S.
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The Legendre operator function
Izvestiya: Mathematics, 2001The paper considers the abstract Cauchy problem (ACO) \[ L_k u(t) \equiv u''(t)+ \gamma k\text{\,coth\,}\gamma t\,u'(t)+ (\gamma k/2)^2 u(t)= Au(t),\quad t> 0,\quad u(0) = u_0,\quad u'(0)= 0, \] where \(k> 0\), \(\gamma> 0\) and \(A\) is a closed linear operator with a dense domain \(D(A)\) in a Banach space \(E\).
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Operator Hölder–Zygmund Functions
It is well known that a Lipschitz function on the real line does not have to be operator Lipschitz. We show that the situation changes dramatically if we pass to Hölder classes. Namely, we prove that if $f$ belongs to the Hölder class $Ł_\a(\R)$ with $00$.
Aleksandrov, A.B., Peller, V.V.
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