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Titlebook: An Introduction to Modern Analysis; Vicente Montesinos,Peter Zizler,Václav Zizler Textbook 2015 Springer International Publishing Switzerl

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Hans-Ernst Schwiete,Rainer Gauglitzional to those we handled in the first chapters of this text. Functional analysis helps in solving these problems by providing additional powerful tools that work in general contexts, allowing in this way to treat a large variety of situations looking at them from a unifying point of view.
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Excursion to Functional Analysis,ional to those we handled in the first chapters of this text. Functional analysis helps in solving these problems by providing additional powerful tools that work in general contexts, allowing in this way to treat a large variety of situations looking at them from a unifying point of view.
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Translations- und Verlagerungshypothese,onometric functions, i.e., the nowadays called .., a series of the form .. This aim may look difficult to achieve, since . is not, in general, .-periodic, while trigonometric functions are. This is not a big problem if . is supposed to be defined on a closed and bounded interval.
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Metric Spaces,sed in the notion of an ., also called a .. Most interestingly, this notion—an inner product— is powerful enough to induce also a distance, and so the frame in which metric geometry can be done naturally is settled (see Sect. .).
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