The Theory of Generalised Functions [Paperback]

Starting from an elementary level Professor Jones discusses generalised functions and their applications.Starting from an elementary level Professor Jones discusses generalised functions and their applications. He aims to supply the simplest introduction for those who wish to learn to use generalised functions and there is liberal provision of exercises with which to gain experience.Starting from an elementary level Professor Jones discusses generalised functions and their applications. He aims to supply the simplest introduction for those who wish to learn to use generalised functions and there is liberal provision of exercises with which to gain experience.Starting from an elementary level Professor Jones discusses generalised functions and their applications. He aims to supply the simplest introduction for those who wish to learn to use generalised functions and there is liberal provision of exercises with which to gain experience. The study of more advanced topics such as partial differential equations, Laplace transforms and ultra-distributions should also make it a valuable source for researchers. The demands placed upon the reader's analytical background are the minimum required to approach this topic. Therefore, by selecting chapters it is possible to construct a short introductory course for students, a final-year option for honours undergraduates or a comprehensive postgraduate course.1. Convergence; 2. Good functions; 3. Generalised functions; 4. Powers of x; 5. Series; 6. Multiplication and the convolution product; 7. Several variables; 8. Change of variables and related topics; 9. Asymptotic behaviour of Fourier integrals; 10. Some applications; 11. Weak functions; 12. The Laplace transform.