Two variable subnormal completion problem

A New Approach to the 2-variable Subnormal Completion Problem

Abstract. We study the Subnormal Completion Problem (SCP) for 2-variable weighted shifts. We use tools and techniques from the theory of truncated moment problems to give a general strategy to solve SCP. We then show that when all quadratic moments are known (equivalently, when the initial segment of weights consists of five independent data points), the natural necessary conditions for the exi...

A Subnormal Toeplitz Completion Problem

We give a brief survey of subnormality and hyponormality of Toeplitz operators on the vector-valued Hardy space of the unit circle. We also solve the following subnormal Toeplitz completion problem: Complete the unspecified rational Toeplitz operators (i.e., the unknown entries are rational Toeplitz operators) of the partial block Toeplitz matrix

One-step extensions of subnormal 2-variable weighted shifts

Two agents single machine scheduling problem with total completion time and total weighted completion time objectives

NP-hardness of the single-variable-resource scheduling problem to minimize the total weighted completion time

Baker and Nuttle [1] studied the following single-variable-resource scheduling problem: sequencing n jobs for processing by a single resource to minimize a function of job completion times, when the availability of the resource varies over time. When the objective function to be minimized is the total weighted completion time, Baker and Nuttle conjectured that the problem is NP-hard. We show in...