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The purpose of this book is to present some basic results in analysis that canbe used to solve various problems, so it may serve as a kind of toolbox. We donot intend to give a complete panorama of the field. In particular, we concentrateon real analysis and leave complex analysis aside; however we consider complexfunctions now and then. Although we cannot claim that this volume is devoted toapplied analysis, our choice of topics is driven by our wish to present results thatcan be applied to concrete problems. It is in this sense that this book could be called“Motivated Analysis”. This expression is due to J.-P. Aubin and means that we shallgather some results of analysis that may be useful in applications, even if the natureof these applications is not the focus of the text. Thus, our route is not the choice ofsome important problems that occur in applications, as in [22, 62, 87, 88, 101, 129,130, 140, 178, 191, 236, 241, 245], but neither is it the panorama of deep advancesin mathematical concepts presented in [100] and [101]. |
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