Titlebook: Analysis and Partial Differential Equations; Thomas Alazard Textbook 2024 The Editor(s) (if applicable) and The Author(s), under exclusive

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978-3-031-70908-1The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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Holistic Multimodal Interaction and Designe and powerful theory: the study of Hilbert spaces. These are the spaces for which we have an analogue of Pythagoras’ theorem, so we can use the methods of Euclidean geometry in infinite-dimensional spaces. We will study the properties of orthogonality and convexity and see how they intervene in the

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https://doi.org/10.1007/978-3-031-17615-9e refer to the beautiful texts of Jean-Pierre Kahane [90, 91, 93]. He is mainly known for having introduced the decomposition of a periodic function into an infinite sum of trigonometric functions of frequencies each of which is a multiple of a fundamental frequency. He had conjectured that every fu

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Yali Chen,Zhenxi Gong,Qiyan Xing the local averages of a function: the convolution product . and the maximal function . (.). These two tools will allow us to study the approximations of the identity introduced by Friedrichs and to prove fundamental inequalities due to Hardy, Littlewood and Sobolev. In the last two sections,we will

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Fixed Point Theoremsnal vector space.We will see several situations in whichwe can guarantee the existence of a solution and also obtain the solution as the limit of a sequence defined iteratively. We will prove several fundamental results: the Banach fixed point theorem, the local inversion theorem, the Cauchy–Lipschi

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