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The elementary theory of distributions (II)

100%
Mikusiński J., Sikorski R.
Instytut Matematyczny Polskiej Akademii Nauk
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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The elementary theory of distributions (I)

100%
Mikusiński J., Sikorski R.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS Introduction........................................................................................................... 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......................................................................... 51 References............................................................................................................ 54
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On some classes of infinitely decomposable Sobolev-Schwartz test functions

74%
Mikusiński J.
Annales Polonici Mathematici
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1985
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tom 46
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nr 1
193-195
4
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Einige Bemerkungen über die Hirschman-Widder'schen Funktionen $H_{n,k}(x)$

66%
Łuszczki Z., Mikusiński J., Urbanik K., Wloka J., Zieleźny Z.
Colloquium Mathematicum
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1956-1957
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tom 4
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nr 1
30-32
5
Content available remote

Weak integrals defined on Euclidean n-space

56%
Brooks J. K., Mikusiński J.
Studia Mathematica
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1972
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tom 44
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nr 5
501-505
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