Fumiko Futamura

Localizable operators and the construction of localized frames

We introduce the notion of localizable operators with respect to frames and prove the boundedness of such operators on families of Banach spaces. This generalizes previous results for specific operators, such as pseudo-differential operators on modulation spaces. We also use this notion to provide sufficient conditions for the construction of frames which have the localization property.

Taking Mathematics Abroad: A How-To Guide

Abstract This paper summarizes the experiences of two mathematics faculty members who participated in an in-house study abroad program. Descriptions of math courses taught abroad are given, as well as how students were recruited, courses were designed, and the environment was incorporated. Tips for mathematics faculty wanting to offer study abroad are given and impacts on the students are discussed.

A New Perspective on Finding the Viewpoint

Summary We take a fresh perspective on an old idea and create an alternate way to answer the question: where should we stand in front of an image in two-point perspective to view it correctly? We review known geometric and algebraic techniques, then use the cross ratio to derive a simple algebraic formula and a technique that makes use of slopes on a perspective grid.

The cross ratio as a shape parameter for Dürer's solid

On the 500th anniversary of Albrecht Dürers copperplate engraving Melencolia I, we invite readers to join in a time-honoured ‘party game’ that has attracted art historians and scientists for many years: guessing the nature and meaning of the compositions enigmatic stone polyhedron. Our main purpose is to demonstrate the usefulness of the cross ratio in the analysis of works in perspective. We show how the cross ratio works as a projectively invariant ‘shape parameter’ of the polyhedron, and how it can be used in analysing other existing theories.

Localized frames and localizable operators

We introduce the notion of operators localized with respect to frames and prove the boundedness of such operators on families of Banach spaces. This generalizes the method used in proving boundedness of pseudodifferential operators on various spaces. We also use this notion to provide sufficient conditions for the construction of frames which have the localization property.