The elementary theory of distributions (I)

Jan Mikusiński ; Roman Sikorski

GDML_Books, (1957), p.

Résumé

CONTENTS Introduction........................................................................................................... 3 § 1. The abstraction principle............................................................................... 4 § 2. Fundamental sequences of continuous functions......................................... 5 § 3. The definition of distributions........................................................................ 9 § 4. Distributions as a generalization of the notion of functions........................... 11 § 5. Algebraic operations on distributions............................................................ 12 § 6. Derivation of distributions.............................................................................. 13 § 7. The definition of distributions by derivatives................................................. 16 § 8. Locally integrable functions........................................................................... 17 § 9. Sequences and series of distributions.......................................................... 19 § 10. Distributions depending on a continuous parameter................................... 23 § 11. Multiplication of distributions by functions.................................................... 25 § 12. Substitutions................................................................................................ 27 § 13. Equality of distributions in intervals............................................................. 30 § 14. Functions with poles.................................................................................... 32 § 15. Derivative as the limit of a difference quotient............................................. 33 § 16. The value of a distribution at a point............................................................ 35 § 17. Existence theorems for values of distributions............................................. 37 § 18. The value of a distribution at infinity............................................................. 41 § 19. The integral of a distribution......................................................................... 42 § 20. Periodic distributions.................................................................................... 46 § 21. Distributions of infinite order......................................................................... 51 References............................................................................................................ 54

Détail

EUDML-ID : urn:eudml:doc:268381