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Einfhrung in die Funktionalanalysis
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Funktionalanalysis hat sich in den letzten Jahrzehnten zu einer der wesentlichen Grundlagen der modernen angewandten Mathematik entwickelt, von der Theorie und Numerik von Differentialgleichungen ber Optimierung und Wahrscheinlichkeitstheorie bis zu medizinischer Bildgebung und mathematischer Bildverarbeitung. Das vorliegende Lehrbuch bietet eine kompakte Einfhrung in die Theorie und ist begleitend fr eine vierstndige Vorlesung im Bachelorstudium konzipiert. Es spannt den Bogen von den topologischen Grundlagen aus der Analysis-Grundvorlesung bis zur Spektraltheorie in Hilbertrumen; besondere Aufmerksamkeit wird dabei den zentralen Resultaten ber Dualrume und schwache Konvergenz geschenkt.
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