Harmonic analysis، MSC Midterm Exam ،Dr.Vishki

Exam Name : Harmonic analysis

MSC Midterm Exam

Dr H.R.E.Vishki

Department of Mathematics Ferdowsi University of Mashhad

24- Ordibehesht 87

1.

Let

be the left Haar measure on G. show that :
i)

G is compact iff .

ii) G

is unimodulus iff is inversion invariant .
2.

For

As a subgroup of

, construct the left and right Haar measures of G.
3.

For a compact group G, show that .
4.

Show that

is not a .

Construct an approximate identity for .
5.

Let

be the modulus function of G. show that if

then G is unimodulus.