# Topics on Function Spaces and Multilinear Algebra Licentiatavhandling, 2013

The present thesis consists of three different papers. Indeed, they treat two different research areas: function spaces and multilinear algebra. In paper I, a characterization of continuity of the $p$-$\Lambda$-variation function is given and Helly's selection principle for $\Lambda BV^{(p)}$ functions is established. A characterization of the inclusion of Waterman-Shiba classes into classes of functions with given integral modulus of continuity is given. A useful estimate on the modulus of variation of functions of class $\Lambda BV^{(p)}$ is found. In paper II, a characterization of the inclusion of Waterman-Shiba classes into $H_{\omega}^{q}$ is given. This corrects and extends an earlier result of a paper from 2005. In paper III, we discuss the existence of an orthogonal basis consisting of decomposable vectors for all symmetry classes of tensors associated with semi-dihedral groups $SD_{8n}$. The dimensions of these symmetry classes of tensors are also computed.
Euler, Matematiska vetenskaper, Chalmers Tvärgata 3
Opponent: Professor Sandra Pott

## Författare

### Mahdi Hormozi

Chalmers, Matematiska vetenskaper

Göteborgs universitet

### On p-Λ-bounded variation

Bulletin of the Iranian Mathematical Society,; Vol. 37(2011)p. 35-49

Artikel i vetenskaplig tidskrift

### Inclusion of Lambda BV(p) spaces in the classes H-omega(q)

Journal of Mathematical Analysis and Applications,; Vol. 404(2013)p. 195-200

Artikel i vetenskaplig tidskrift

### Symmetry classes of tensors associated with the Semi-Dihedral groups SD8n

Colloquium Mathematicum,; Vol. 131(2013)p. 59-67

Artikel i vetenskaplig tidskrift

### Ämneskategorier

Algebra och logik

Matematisk analys

Euler, Matematiska vetenskaper, Chalmers Tvärgata 3

Opponent: Professor Sandra Pott

2017-10-07