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Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
Introduction...........................................................................................7
Notation...............................................................................................10
1. Auxiliary results in topology..............................................................11
2. Auxiliary results for topological groups............................................17
3. Elementary properties of homomorphism groups............................21
4. Homomorphism groups of abelian metrizable groups......................23
5. Some results in duality theory.........................................................25
6. Locally quasi-convex groups...........................................................30
7. Properties of the quasi-convex hull.................................................36
8. Reflexivity of locally convex vector spaces......................................40
9. Locally convex vector groups..........................................................46
10. Two representations of locally quasi-convex groups.....................48
11. The character groups of $L^p_ℤ([0,1])$ and $L^p([0,1])$............53
12. Free abelian topological groups...................................................58
13. C(K,𝕋) for compact K....................................................................63
14. The group C(X,𝕋)..........................................................................69
15. Duality theory for free abelian topological groups.........................71
16. A short survey of the theory of nuclear groups.............................73
17. Ellipsoids.......................................................................................73
18. Properties of the Kolmogorov diameter.........................................75
19. Gaussian-like measures................................................................86
20. Nuclear groups..............................................................................93
21. An embedding theorem for nuclear groups.................................104
22. The Bochner Theorem for nuclear groups..................................105
References........................................................................................111
Introduction...........................................................................................7
Notation...............................................................................................10
1. Auxiliary results in topology..............................................................11
2. Auxiliary results for topological groups............................................17
3. Elementary properties of homomorphism groups............................21
4. Homomorphism groups of abelian metrizable groups......................23
5. Some results in duality theory.........................................................25
6. Locally quasi-convex groups...........................................................30
7. Properties of the quasi-convex hull.................................................36
8. Reflexivity of locally convex vector spaces......................................40
9. Locally convex vector groups..........................................................46
10. Two representations of locally quasi-convex groups.....................48
11. The character groups of $L^p_ℤ([0,1])$ and $L^p([0,1])$............53
12. Free abelian topological groups...................................................58
13. C(K,𝕋) for compact K....................................................................63
14. The group C(X,𝕋)..........................................................................69
15. Duality theory for free abelian topological groups.........................71
16. A short survey of the theory of nuclear groups.............................73
17. Ellipsoids.......................................................................................73
18. Properties of the Kolmogorov diameter.........................................75
19. Gaussian-like measures................................................................86
20. Nuclear groups..............................................................................93
21. An embedding theorem for nuclear groups.................................104
22. The Bochner Theorem for nuclear groups..................................105
References........................................................................................111
Słowa kluczowe
Tematy
Kategoryzacja MSC:
- 52C07: Lattices and convex bodies in n dimensions
- 22Axx: Topological and differentiable algebraic systems
- 54E15: Uniform structures and generalizations
- 11H06: Lattices and convex bodies
- 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization
- 43A40: Character groups and dual objects
- 54Dxx: Fairly general properties
- 52A40: Inequalities and extremum problems
- 43A35: Positive definite functions on groups, semigroups, etc.
- 46Axx: Topological linear spaces and related structures
- 22B99: None of the above, but in this section
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
384
Liczba stron
113
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCLXXXIV
Daty
wydano
1999
otrzymano
1998-12-16
poprawiono
1999-09-02
Twórcy
autor
- Mathematisches Institut der Universität, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
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Języki publikacji
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Uwagi
1991 Mathematics Subject Classification: 11H06, 22Axx, 22B99, 43A40, 43A35, 46Axx, 52C07, 52A40, 54Dxx, 54E15, 60B15.
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DML-PL
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