Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world's leading mathematical journals. Without specializing in a small number of subject areas, it emphasizes the most active and influential areas of current mathematics.

### Volume 58, Number 1

#### Publication Date: February 1989

José Luis Rubio de Francia; 1-19

The disc multiplier

A. Córdoba; 21-29

Algebraic cycles on nonsimple abelian varieties

Fumio Hazama; 31-37

Moduli spaces of degree $d$ hypersurfaces in $\mathbb{P}_n$

Frances Kirwan; 39-78

On varieties isomorphic in codimension one to torus embeddings

Jonathan Fine; 79-88

A decomposition theorem for certain self-dual modules in the category $\mathcal{O}$

David H. Collingwood and Ronald S. Irving; 89-102

Spectral analysis of second-order elliptic operators on noncompact manifolds

Richard Froese and Peter Hislop; 103-129

Isospectral sets of conformally equivalent metrics

Robert Brooks, Peter Perry and Paul Yang; 131-150

A classification of invariant knots

Monica Nicolau; 151-171

Bounded imbeddings of open Kähler manifolds in $C^N$

John S. Bland; 173-203

Nonlocal inversion formulas for the X-ray transform

Allan Greenleaf and Gunther Uhlmann; 205-240

Homological properties of periodic homeomorphisms of $4$-manifolds

Sławomir Kwasik and Reinhard Schultz; 241-250

Translates of functions of two variables

Håkan Hedenmalm; 251-297