The elementary theory of distributions (I)

Jan Mikusiński; Roman Sikorski

  • 1957

Abstract

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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

How to cite

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Jan Mikusiński, and Roman Sikorski. The elementary theory of distributions (I). 1957. <http://eudml.org/doc/268381>.

@book{JanMikusiński1957,
abstract = {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},
author = {Jan Mikusiński, Roman Sikorski},
keywords = {Functional Analysis; Abstract Spaces},
language = {eng},
title = {The elementary theory of distributions (I)},
url = {http://eudml.org/doc/268381},
year = {1957},
}

TY - BOOK
AU - Jan Mikusiński
AU - Roman Sikorski
TI - The elementary theory of distributions (I)
PY - 1957
AB - 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
LA - eng
KW - Functional Analysis; Abstract Spaces
UR - http://eudml.org/doc/268381
ER -

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