Taylor formula for distributions

Bogdan Ziemian

GDML_Books, (1988), p.

Résumé

CONTENTS0. Introduction................................................................................................................................................................51. Preliminary remarks...................................................................................................................................................62. Hyperfunctions and their generalizations.................................................................................................................103. Flat functions; definitions and properties.................................................................................................................144. Taylor formula for quasi $O(x^a)$ functions.............................................................................................................185. Homogeneous distributions and their properties......................................................................................................206. Mellin transformable distributions.............................................................................................................................227. Differential equations in the space of Mellin transformable distributions. Operational calculus for ℳ......................268. Taylor formula for distributions.................................................................................................................................299. Taylor transformation for functions and distributions................................................................................................3210. Spectral support of a function and of a distribution................................................................................................3311. Determination of singularities of solutions of ordinary linear differential operators with smooth coefficients..........3611. 1. Asymptotic expansion of the push-forward operation $F_{∗}φ$ for F admitting an F-invariant operator...........4012. Value of a function (distribution) at a point.............................................................................................................4113. Taylor formula for the product of functions.............................................................................................................4414. Multiplication of distributions. Taylor formula for the product of distributions..........................................................4714.1. Spectral topology................................................................................................................................................5014.2. Heuristic remarks concerning multiplication of distributions.................................................................................5114.3. Taylor formula for the function 1/f........................................................................................................................5115. Taylor formula for composite functions...................................................................................................................52References ..................................................................................................................................................................56

Détail

Zbl 0685.46025

EUDML-ID : urn:eudml:doc:268619