The elementary theory of distributions (II)

Jan Mikusiński; Roman Sikorski

  • 1961

Abstract

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CONTENTS Introduction................................................................................... 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

How to cite

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Jan Mikusiński, and Roman Sikorski. The elementary theory of distributions (II). 1961. <http://eudml.org/doc/268348>.

@book{JanMikusiński1961,
abstract = {CONTENTS Introduction................................................................................... 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 = {Jan Mikusiński, Roman Sikorski},
keywords = {functional analysis},
language = {eng},
title = {The elementary theory of distributions (II)},
url = {http://eudml.org/doc/268348},
year = {1961},
}

TY - BOOK
AU - Jan Mikusiński
AU - Roman Sikorski
TI - The elementary theory of distributions (II)
PY - 1961
AB - CONTENTS Introduction................................................................................... 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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