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"Higher mathematics" once pointed towards the involvement of infinity. This we label analysis. The ancient Greeks had helped it to a first high point when they mastered the infinite. The book traces the history of analysis along the risky route of serial procedures through antiquity. It took quite long for this type of mathematics to revive in our region. When and where it did, infinite series proved the driving force. Not until a good two millennia had gone by, would analysis head towards Greek rigor again. To follow all that trial, error and final accomplishment, is more than studying history: It provides touching, worthwhile access to advanced calculus. Moreover, some steps beyond convergence show infinite series to naturally fit a wider frame.

Series, Infinite. --- Mathematics --- Math --- Science --- Infinite series --- Philosophy --- History.

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The Tauberian theory has found a widespread application in probability theory. Despite the strong interest of probabilists in Tauberian theorems, no book specially devoted to this topic has been published yet. This monograph is intended to fill this gap.

Tauberian theorems. --- Laplace transformation. --- Differential equations, Elliptic. --- Elliptic differential equations --- Elliptic partial differential equations --- Linear elliptic differential equations --- Differential equations, Linear --- Differential equations, Partial --- Transformation, Laplace --- Calculus, Operational --- Differential equations --- Transformations (Mathematics) --- Series, Infinite

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Spectral synthesis

Functional analysis --- Differential equations --- Locally compact Abelian groups --- Spectral synthesis (Mathematics) --- Tauberian theorems --- #KVIV --- #WWIS:STAT --- 517.518.1 --- 517.518.1 Measure. Integration. Differentiation --- Measure. Integration. Differentiation --- Series, Infinite --- Synthesis, Spectral (Mathematics) --- Group theory --- Harmonic analysis --- Spectral theory (Mathematics) --- Compact Abelian groups --- Locally compact groups --- Topological groups --- Spectral synthesis (Mathematics). --- Locally compact Abelian groups. --- Tauberian theorems. --- 517.5 --- Banach, Algèbres de --- Fourier, Analyse de --- Banach, Algèbres de --- Théorèmes taubériens --- 517.5 Theory of functions --- Theory of functions