Książka - szczegóły

CONTENTS
0. Introduction................................................................................................................................................................5
1. Preliminary remarks...................................................................................................................................................6
2. Hyperfunctions and their generalizations.................................................................................................................10
3. Flat functions; definitions and properties.................................................................................................................14
4. Taylor formula for quasi $O(x^a)$ functions.............................................................................................................18
5. Homogeneous distributions and their properties......................................................................................................20
6. Mellin transformable distributions.............................................................................................................................22
7. Differential equations in the space of Mellin transformable distributions. Operational calculus for ℳ......................26
8. Taylor formula for distributions.................................................................................................................................29
9. Taylor transformation for functions and distributions................................................................................................32
10. Spectral support of a function and of a distribution................................................................................................33
11. Determination of singularities of solutions of ordinary linear differential operators with smooth coefficients..........36
11. 1. Asymptotic expansion of the push-forward operation $F_{∗}φ$ for F admitting an F-invariant operator...........40
12. Value of a function (distribution) at a point.............................................................................................................41
13. Taylor formula for the product of functions.............................................................................................................44
14. Multiplication of distributions. Taylor formula for the product of distributions..........................................................47
14.1. Spectral topology................................................................................................................................................50
14.2. Heuristic remarks concerning multiplication of distributions.................................................................................51
14.3. Taylor formula for the function 1/f........................................................................................................................51
15. Taylor formula for composite functions...................................................................................................................52
References ..................................................................................................................................................................56