| 書目名稱 | Operator Relations Characterizing Derivatives | | 編輯 | Hermann K?nig,Vitali Milman | | 視頻video | http://file.papertrans.cn/703/702322/702322.mp4 | | 概述 | Develops an operator viewpoint for functional equations in classical function spaces of analysis.Demonstrates the rich, operator-type structure behind the fundamental notion of the derivative and its | | 圖書封面 |  | | 描述 | .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 Ck-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. TheLeibniz rule, the Chain rule and its extensions turn out to be stable under perturbations and relaxations of assumptions on the form of the operators. The results yield an algebraic understanding of first- and se | | 出版日期 | Book 2018 | | 關(guān)鍵詞 | Laplacian; Leibniz rule; chain rule; operator equation; C^k-spaces; localization; stability | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-00241-1 | | isbn_softcover | 978-3-030-13096-1 | | isbn_ebook | 978-3-030-00241-1 | | copyright | Springer Nature Switzerland AG 2018 |
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