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Compact Abelian groups and extensions of Haar measures

100%

Hulanicki A.

Instytut Matematyczny Polskiej Akademii Nauk

EN

Contents Introduction.................................................................................................................... 3 1. Preliminaries (topology & measure).................................................................... 3 2. Problems and the theorem.................................................................................... 7 3. Preliminaries (abstract groups, Cartesian products)....................................... 9 4. Preliminaries (automorphisms, duality theory).................................................. 13 5. Compact groups....................................................................................................... 15 6. Theorems on the groups $D_p$........................................................................... 18 7. A decomposition of compact groups.................................................................... 27 8. Groups in which all compact topologies are isomorphic................................ 33 9. The class M............................................................................................................... 40 10. Proof of the Main Theorem (groups of the class M)........................................ 42 11. Proof of tho Main Theorem (reduced groups).................................................. 47 12. Proof of the Main Theorem (conclusion)........................................................... 48 References.................................................................................................................... 57

2

The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group

83%

Hulanicki A.

Studia Mathematica

|

1976

|

tom 56

|

nr 2

165-173

3

The structure of the factor group of the unrestricted sum by the restricted sum of Abelian groups II

48%

Golema K., Hulanicki A.

Fundamenta Mathematicae

|

1964

|

tom 53

|

nr 2

177-185

4

Algebraic characterization of abelian divisible groups which admit compact topologies

48%

Hulanicki A.

Fundamenta Mathematicae

|

1957

|

tom 44

|

nr 2

192-197

5

Sur les ensembles denses de puissance minimum dans les groupes topologiques

42%

Hartman S., Hulanicki A.

Colloquium Mathematicum

|

1958

|

tom 6

|

nr 1

187-191

6

On commutative approximate identities and cyclic vectors of induced representations

42%

Hulanicki A., Pytlik T.

Studia Mathematica

|

1973

|

tom 48

|

nr 2

189-199

7

Groups whose regular representation weakly contains all unitary representations

42%

Hulanicki A.

Studia Mathematica

|

1964

|

tom 24

|

nr 1

27-59

8

On the topological structure of 0-dimensional topological groups

42%

Hulanicki A.

Fundamenta Mathematicae

|

1958-1959

|

tom 46

|

nr 3

317-320

9

Subalgebra of $L_1(G)$ associated with Laplacian on a Lie group

42%

Hulanicki A.

Colloquium Mathematicum

|

1974

|

tom 31

|

nr 2

259-287

10

Invariant subsets of nonsynthesis Leptin algebras and nonsymmetry

42%

Hulanicki A.

Colloquium Mathematicum

|

1980

|

tom 43

|

nr 1

127-136

11

Invariant extensions of the Haar measure

36%

Hulanicki A., Ryll-Nardzewski C.

Colloquium Mathematicum

|

1979

|

tom 42

|

nr 1

223-227

12

On the spectrum of the Laplacian on the affine group of the real line

36%

Hulanicki A.

Studia Mathematica

|

1975-1976

|

tom 54

|

nr 3

199-204

13

On positive functionals on a group algebra multiplicative on a subalgebra

36%

Hulanicki A.

Studia Mathematica

|

1970-1971

|

tom 37

|

nr 2

163-171

14

The completeness of the homeomorphisms group of a complete space

36%

Hulanicki A.

Colloquium Mathematicum

|

1957-1958

|

tom 5

|

nr 2

159-161

15

On locally compact topological groups of power of continuum

36%

Hulanicki A.

Fundamenta Mathematicae

|

1957

|

tom 44

|

nr 2

156-158

16

Les sous-groupes purs et leurs duals

30%

Hartman S., Hulanicki A.

Fundamenta Mathematicae

|

1958

|

tom 45

|

nr 1

71-77

17

Isomorphic embeddings of free products of compact groups

30%

Hulanicki A.

Colloquium Mathematicum

|

1967

|

tom 16

|

nr 1

235-241

18

Means and Følner condition on locally compact groups

30%

Hulanicki A.

Studia Mathematica

|

1966

|

tom 27

|

nr 2

87-104

19

On symmetry of group algebras of discrete nilpotent groups

30%

Hulanicki A.

Studia Mathematica

|

1970

|

tom 35

|

nr 2

207-219

20

Invariant extensions of the Lebesgue measure

30%

Hulanicki A.

Fundamenta Mathematicae

|

1962

|

tom 51

|

nr 2

111-115

Ograniczanie wyników

Compact Abelian groups and extensions of Haar measures

The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group

The structure of the factor group of the unrestricted sum by the restricted sum of Abelian groups II

Algebraic characterization of abelian divisible groups which admit compact topologies

Sur les ensembles denses de puissance minimum dans les groupes topologiques

On commutative approximate identities and cyclic vectors of induced representations

Groups whose regular representation weakly contains all unitary representations

On the topological structure of 0-dimensional topological groups

Subalgebra of $L_1(G)$ associated with Laplacian on a Lie group

Invariant subsets of nonsynthesis Leptin algebras and nonsymmetry

Invariant extensions of the Haar measure

On the spectrum of the Laplacian on the affine group of the real line

On positive functionals on a group algebra multiplicative on a subalgebra

The completeness of the homeomorphisms group of a complete space

On locally compact topological groups of power of continuum

Les sous-groupes purs et leurs duals

Isomorphic embeddings of free products of compact groups

Means and Følner condition on locally compact groups

On symmetry of group algebras of discrete nilpotent groups

Invariant extensions of the Lebesgue measure