Christian Clason

Das vorliegende Lehrbuch bietet eine kompakte Einführung in die Theorie der Funktionalanalysis und ist begleitend für eine vierstündige Vorlesung im Bachelorstudium konzipiert. Es spannt den Bogen von den topologischen Grundlagen aus der Analysis-Grundvorlesung bis zur Spektraltheorie in Hilberträumen; besondere Aufmerksamkeit wird dabei den zentralen Resultaten über Dualräume und schwache Konvergenz geschenkt. In dieser zweiten Auflage wurden Fehler korrigiert und die Darstellung an einigen Stellen verbessert. Zusätzlich wurden die Aufgaben insbesondere um eine Sammlung von Lernzielfragen als Hilfestellung für das Selbststudium oder für die Prüfungsvorbereitung ergänzt.

Functional analysis has become one of the essential foundations of modern applied mathematics in the last decades, from the theory and numerical solution of differential equations, from optimization and probability theory to medical imaging and mathematical image processing. This textbook offers a compact introduction to the theory and is designed to be used during one semester, fitting exactly 26 lectures of 90 minutes each. It ranges from the topological fundamentals recalled from basic lectures on real analysis to spectral theory in Hilbert spaces. Special attention is given to the central results on dual spaces and weak convergence.

War of the Zealot Empire #3 - Vesuvius is on the rise and his vision could not be clearer. Since the fall of the Prophet, the Empire fell, but he has made it his duty to eradicate all in his way of social order, domination and control. From Medelthians to rebels among his own species, he will stop at nothing to restore order amongst the gross chaos that has befallen his people. But when he meets the most savage of women, a woman who could ruthlessly beat him to death without batting an eye, his heart stops. Everything about the world he knew was upside down, and between their survival and teh feelings in his soul and body, he cannot stand to be away from her. After all, if not for the protection of a dragon, he would be a vatulure's snack.

Book 2 of War of the Zealot Empire Telemechus has waited ten long years since he returned to the Zealot Empire. Now, he has a chance to return to a place where he feels alive, where he has true friends and a better destiny. It is now his destiny to rebuild friendships of old, which have faded over the years. He has one heart and not much to lose when he goes head over heels for a new love. But the Matriarchs, the goddesses of his people and the last females, are in danger and there are few options to save them. With the oppression of terran values among the Empire, there are fewer options for Tiberius, who finds himself not only questioning his previously neutral views about the world and about a particularly interesting girl. Even Medelthian views are pulled into question as the civil war arises another civil war within the Zealot Empire, tearing between the zealots with the fall of the Prophet; a cross between terran friends and foes.