The elementary theory of distributions (II)

J. Mikusiński; R. Sikorski

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1961

Abstract

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CONTENTSIntroduction................................................................................... 3§ 1. Terminology and notation.................................................................................... 4§ 2. Uniform and almost uniform convergence....................................................... 6§ 3. Fundamental sequences of smooth functions............................................... 6§ 4. The definition of distributions............................................................................. 7§ 5. Multiplication by a number................................................................................... 8§ 6. Addition................................................................................................................... 9§ 7. Regular operations............................................................................................. 10§ 8. Subtraction, translation, derivation................................................................... 11§ 9. Multiplication of a distribution by a smooth function...................................... 11§ 10. Substitution......................................................................................................... 12§ 11. Product of distributions with separated variables....................................... 13§ 12. Convolution by a smooth function vanishing outside an interval.............. 14§ 13. Calculations with distributions........................................................................ 16§ 14. Delta-sequences and delta-distribution........................................................ 17§ 15. Distributions in subsets.................................................................................... 19§ 16. Distributions as a generalization of the notion of continuous functions.. 19§ 17. Operations on continuous functions............................................................... 21§ 18. Locally integrable functions.............................................................................. 24§ 19. Operations on locally integrable functions.................................................... 25§ 20. Sequences of distributions............................................................................... 27§ 21. Convergence and regular operations............................................................. 30§ 22. Distributionally convergent sequences of smooth functions...................... 32§ 23. Locally convergent sequences of distributions............................................. 34§ 24. Distributions depending on a continuous parameter.................................. 36§ 25. Multidimensional substitution........................................................................... 37§ 26. Distributions constant in some variables....................................................... 39§ 27. Dimension of distributions................................................................................. 41§ 28. Distributions with vanishing m-th derivatives................................................. 44

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J. Mikusiński, and R. Sikorski. The elementary theory of distributions (II). Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1961. <http://eudml.org/doc/268348>.

@book{J1961,
abstract = {CONTENTSIntroduction................................................................................... 3§ 1. Terminology and notation.................................................................................... 4§ 2. Uniform and almost uniform convergence....................................................... 6§ 3. Fundamental sequences of smooth functions............................................... 6§ 4. The definition of distributions............................................................................. 7§ 5. Multiplication by a number................................................................................... 8§ 6. Addition................................................................................................................... 9§ 7. Regular operations............................................................................................. 10§ 8. Subtraction, translation, derivation................................................................... 11§ 9. Multiplication of a distribution by a smooth function...................................... 11§ 10. Substitution......................................................................................................... 12§ 11. Product of distributions with separated variables....................................... 13§ 12. Convolution by a smooth function vanishing outside an interval.............. 14§ 13. Calculations with distributions........................................................................ 16§ 14. Delta-sequences and delta-distribution........................................................ 17§ 15. Distributions in subsets.................................................................................... 19§ 16. Distributions as a generalization of the notion of continuous functions.. 19§ 17. Operations on continuous functions............................................................... 21§ 18. Locally integrable functions.............................................................................. 24§ 19. Operations on locally integrable functions.................................................... 25§ 20. Sequences of distributions............................................................................... 27§ 21. Convergence and regular operations............................................................. 30§ 22. Distributionally convergent sequences of smooth functions...................... 32§ 23. Locally convergent sequences of distributions............................................. 34§ 24. Distributions depending on a continuous parameter.................................. 36§ 25. Multidimensional substitution........................................................................... 37§ 26. Distributions constant in some variables....................................................... 39§ 27. Dimension of distributions................................................................................. 41§ 28. Distributions with vanishing m-th derivatives................................................. 44},
author = {J. Mikusiński, R. Sikorski},
keywords = {functional analysis},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {The elementary theory of distributions (II)},
url = {http://eudml.org/doc/268348},
year = {1961},
}

TY - BOOK
AU - J. Mikusiński
AU - R. Sikorski
TI - The elementary theory of distributions (II)
PY - 1961
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - CONTENTSIntroduction................................................................................... 3§ 1. Terminology and notation.................................................................................... 4§ 2. Uniform and almost uniform convergence....................................................... 6§ 3. Fundamental sequences of smooth functions............................................... 6§ 4. The definition of distributions............................................................................. 7§ 5. Multiplication by a number................................................................................... 8§ 6. Addition................................................................................................................... 9§ 7. Regular operations............................................................................................. 10§ 8. Subtraction, translation, derivation................................................................... 11§ 9. Multiplication of a distribution by a smooth function...................................... 11§ 10. Substitution......................................................................................................... 12§ 11. Product of distributions with separated variables....................................... 13§ 12. Convolution by a smooth function vanishing outside an interval.............. 14§ 13. Calculations with distributions........................................................................ 16§ 14. Delta-sequences and delta-distribution........................................................ 17§ 15. Distributions in subsets.................................................................................... 19§ 16. Distributions as a generalization of the notion of continuous functions.. 19§ 17. Operations on continuous functions............................................................... 21§ 18. Locally integrable functions.............................................................................. 24§ 19. Operations on locally integrable functions.................................................... 25§ 20. Sequences of distributions............................................................................... 27§ 21. Convergence and regular operations............................................................. 30§ 22. Distributionally convergent sequences of smooth functions...................... 32§ 23. Locally convergent sequences of distributions............................................. 34§ 24. Distributions depending on a continuous parameter.................................. 36§ 25. Multidimensional substitution........................................................................... 37§ 26. Distributions constant in some variables....................................................... 39§ 27. Dimension of distributions................................................................................. 41§ 28. Distributions with vanishing m-th derivatives................................................. 44
LA - eng
KW - functional analysis
UR - http://eudml.org/doc/268348
ER -

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