Operator Functional Equations in Analysis

DOI10.1007/978-1-4614-6406-8_8zbMath1266.39024OpenAlexW86099075MaRDI QIDQ4928669

Vitali D. Milman, Hermann Koenig

Publication date: 17 June 2013

Published in: Asymptotic Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4614-6406-8_8

zbMATH Keywords

Fourier transformsLeibniz rulemultiplicative mapsChain ruleOperator equations

Mathematics Subject Classification ID

Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Functional equations for real functions (39B22)

Related Items (3)

Disjointness Preservers and Banach-Stone Theorems ⋮ On Rubel type operator equations on the space of analytic functions ⋮ A description of derivation operators with respect to convolution of generalized Gel'fond-Leont'ev integration

Cites Work

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• Characterizing the derivative and the entropy function by the Leibniz rule
• A functional equation characterizing the second derivative
• The chain rule as a functional equation
• Multiplicative derivations on \(C(X)\)
• A characterization of product preserving maps with applications to a characterization of the Fourier transform
• Rigidity and stability of the Leibniz and the chain rule
• Multiplicative semigroups of continuous functions
• An operator equation characterizing the Laplacian
• On Multiplicative Maps of Continuous and Smooth Functions
• An Operator Equation Generalizing the Leibniz Rule for the Second Derivative

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