1. Distributions in the Development of Functional Analysis. - 2. Generalized Differentiation and Generalized Solutions to Differential Equations. - 1. Early Period. The Vibrating String. - 2. The Age of Rigour. - 3. The Fundamental Theorem of the Calculus and the Determination of Areas of Surfaces. - 4. The Calculus of Variations. - 5. Generalized Solutions to Differential Equations. Potential Theory. - 6. Generalized Solutions to Hyperbolic Partial Differential Equations. The Cauchy Problem. - 7. Differential Operators in Hilbert Spaces. - 8. Sobolev's Functionals. - 9. Methods. A Survey. - 3. Generalized Fourier Transforms. - 4. Early Generalized Functions. - 1. Fundamental Solutions. Green's Function. - 2. The ?-function. - 5. De Rham's Currents. - 6. Schwartz' Creation of the Theory of Distributions. - Concluding Remarks. - Appendix. Alternative Definitions of Generalized Functions. - Notes. - Chart I. - Chart II. Language: English
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