Książka - szczegóły

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