Operator Relations Characterizing Derivatives. 1st ed. 2018

種類:

電子ブック

責任表示:

by Hermann König, Vitali Milman

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2018

著者名:

• König, Hermann.
• Milman, Vitali.
• SpringerLink (Online service)

ISBN:

9783030002411 [3030002411]    

注記:

Introduction -- Regular Solutions of Some Functional Equations -- The Leibniz Rule -- The Chain Rule -- Stability and Rigidity of the Leibniz and the Chain Rules -- The Chain Rule Inequality and its Perturbations -- The Second-Order Leibniz rule -- Non-localization Results -- The Second-Order Chain Rule -- Bibliography -- Subject Index -- Author Index.
This monograph develops an operator viewpoint for functional equations in classical function spaces of analysis, thus filling a void in the mathematical literature. Major constructions or operations in analysis are often characterized by some elementary properties, relations or equations which they satisfy. The authors present recent results on the problem to what extent the derivative is characterized by equations such as the Leibniz rule or the Chain rule operator equation in C^k-spaces. By localization, these operator equations turn into specific functional equations which the authors then solve. The second derivative, Sturm-Liouville operators and the Laplacian motivate the study of certain "second-order" operator equations. Additionally, the authors determine the general solution of these operator equations under weak assumptions of non-degeneration. In their approach, operators are not required to be linear, and the authors also try to avoid continuity conditions. The Leibniz rule, the Chain rule and it

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