“Submultiplicativity of Norms for Spaces of Generalized BV-functions,” an article by Robert Kantrowitz ’82, professor and chair of mathematics, was published in the current issue of Real Analysis Exchange.
Functions of bounded variation, or BV-functions, have played a role in various aspects of mathematical analysis for more than a century. Their main influence is in connection with the study of Fourier series and integration theory. The notion of bounded variation has undergone generalizations in several directions. In his paper, Kantrowitz provides an argument for a result describing the interaction between the norm and pointwise products in certain spaces of functions of generalized bounded variation. As a consequence, such functions are seen to have an additional layer of algebraic and analytic structure.