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The elementary theory of distributions (II)

Seria
Rozprawy Matematyczne tom/nr w serii: 25 wydano: 1961
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EN

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
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Seria
Rozprawy Matematyczne tom/nr w serii: 25
Liczba stron
48
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Opis fizyczny
Rozprawy Matematyczne, Tom XXV
Daty
wydano
1961
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Bibliografia
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EN
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bwmeta1.element.zamlynska-bc3c8425-77e8-45c7-9c86-9cbbee296438
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DML-PL
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