English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let X={lambda1, ..., lambdaN} be a finite set of complex numbers, and let A be a normal operator with spectrum X that acts on a separable Hilbert space H. Relative to a fixed orthonormal basis e1, e2, ... for H, A gives rise to a matrix whose diagonal is a sequence d=(d1, d2, ...) with the property that each of its terms dn belongs to the convex hull of X. Not all sequences with that property can arise as the diagonal of a normal operator with spectrum X. The case where X is a set of real numbers has received a great deal of attention over the years and is reasonably well (though incompletely) understood. In this work we take up the case in which X is the set of vertices of a convex polygon in . The critical sequences d turn out to be those that accumulate rapidly in X in the sense that Sigmainfinityn=1 dist(dn, X)&lt;infinity. We show that there is an abelian group GammaX, a quotient of R2 by a countable subgroup with concrete arithmetic properties, and a subjective mapping of such sequences d--&gt;s(d)E GammaX with the following property: If s(d) not equal 0, then d is not the diagonal of any such operator A. We also show that while this is the only obstruction when N=2, there are other (as yet unknown) obstructions when N=3.

Diagonals of normal operators with finite spectrum