Abstract
Classical operations in analysis and geometry as derivatives, the Fourier transform, the Legendre transform, multiplicative maps or duality of convex bodies may be characterized, essentially, by very simple properties which may be often expressed as operator equations, like the Leibniz or the chain rule, bijective maps exchanging products with convolutions or bijective order reversing maps on convex functions or convex bodies. We survey and discuss recent results of this type in analysis. The operations we consider act on classical spaces like C k-spaces or Schwartz spaces \(\mathcal{S}({\mathbb{R}}^{n})\). Naturally, the results strongly depend on the type of the domain and the image space.
Mathematical Subject Classifications (2010): 39B22, 26A24
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Acknowledgements
Hermann König was partially supported by the Fields Institute and Vitali Milman was partially supported by the Minkowski Center at the University of Tel Aviv, by the Fields Institute, by ISF grant 387/09 and BSF grant 2006079.
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König, H., Milman, V. (2013). Operator Functional Equations in Analysis. In: Ludwig, M., Milman, V., Pestov, V., Tomczak-Jaegermann, N. (eds) Asymptotic Geometric Analysis. Fields Institute Communications, vol 68. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6406-8_8
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