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The book aims at giving a monographic presentation of the abstract harmonic analysis of hypergroups, while combining it with applied topics of spectral analysis, approximation by orthogonal expansions and stochastic sequences. Hypergroups are locally compact Hausdorff spaces equipped with a convolution, an involution and a unit element. Related algebraic structures had already been studied by Frobenius around 1900. Their axiomatic characterisation in harmonic analysis was later developed in the 1970s. Hypergoups naturally emerge in seemingly different application areas as time series...

Ausgehend von Vorlesungen an der TU Munchen werden in dem Band die Inhalte der Analysis im 1. und 2. Semester des Mathematik- und Physik-Bachelor-Studiums komplett behandelt. Dazu zahlen neben den Grundlagen der eindimensionalen Analysis auch eine Einfuhrung in die Differenzierbarkeit im Mehrdimensionalen, der Begriff der Konvergenz in metrischen Raumen sowie elementare Losungsmethoden von gewohnlichen Differentialgleichungen. Das Buch bietet motivierende Beispiele und eignet sich sowohl als Nachschlagewerk wie auch als Begleitlekture zur Vorlesung."

This work addresses all of the major topics in Fourier series, emphasizing the concept of approximate identities and presenting applications, particularly in time series analysis. It stresses throughout the idea of homogenous Banach spaces and provides recent results. Techniques from functional analysis and measure theory are utilized. student price, available on request from Marcel Dekker, Inc.