The elementary theory of distributions (I)

J. Mikusiński; R. Sikorski

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1957

Abstract

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CONTENTSIntroduction........................................................................................................... 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......................................................................... 51References............................................................................................................ 54

How to cite

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J. Mikusiński, and R. Sikorski. The elementary theory of distributions (I). Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1957. <http://eudml.org/doc/268381>.

@book{J1957,
abstract = {CONTENTSIntroduction........................................................................................................... 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......................................................................... 51References............................................................................................................ 54},
author = {J. Mikusiński, R. Sikorski},
keywords = {Functional Analysis; Abstract Spaces},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {The elementary theory of distributions (I)},
url = {http://eudml.org/doc/268381},
year = {1957},
}

TY - BOOK
AU - J. Mikusiński
AU - R. Sikorski
TI - The elementary theory of distributions (I)
PY - 1957
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - CONTENTSIntroduction........................................................................................................... 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......................................................................... 51References............................................................................................................ 54
LA - eng
KW - Functional Analysis; Abstract Spaces
UR - http://eudml.org/doc/268381
ER -

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