Synopsis
0. Introduction.- 1. Initial Value Problems in Banach Spaces.- 2. Scales of Banach Spaces.- 3. Solution of Initial Value Problems in Scales of Banach Spaces.- 4. The Classical Cauchy-Kovalevskaya Theorem.- 5. The Holmgren Theorem.- 6. Basic Properties of Generalized Analytic Functions.- 7. Initial Value Problems with Generalized Analytic Initial Functions.- 8. Contraction-Mapping Principles in Scales of Banach Spaces.- 9. Further Existence Theorems for Initial Value Problems in Scales of Banach Spaces.- 10. Further Uniqueness Theorems.- References.
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