Joseph Rosenblatt

The Structure of Homometric Sets

One of the fundamental problems of phase retrieval in spectroscopic analysis is of a combinatorial nature and can be solved using purely algebraic techniques. Given two sets A and B in some Euclidean space

Ergodic Theory and its Connections with Harmonic Analysis: Pointwise ergodic theorems via harmonic analysis

R^n

Square functions in ergodic theory

, A and B are homometric if the sets of vector differences

Oscillation in ergodic theory: Higher dimensional results

\{ x - y:x,y \in A \}

Rigidity and non-recurrence along sequences

and

UNIVERSALLY BAD SEQUENCES IN ERGODIC THEORY

\{ x - y:x,y \in B \}

Invariant means and invariant ideals in L∞(G) for a locally compact group G

are identical counting multiplicities. More generally, given two finite sums

Linear independence of translations

A = \sum a_x \delta _x

A distal property of groups and the growth of connected locally compact groups

and

Oscillation inequalities for rectangles

B = \sum a_x \delta _x