# ANU Mathematical Sciences Institute (MSI)

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The Mathematical Sciences Institute (formerly the School of Mathematical Sciences) was established in 1989 with the aim of unifying the study of mathematics across The Australian National University. MSI publishes conference and symposia proceedings as well as monographs in the **Proceedings of the Centre for Mathematics and Its Applications (formerly the Proceedings of the Centre for Mathematical Analysis).**

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Item Open Access Boundedness of maximal operators and maximal commutators on non-homogenous spaces(The Australian National University, Mathematical Sciences Institute, Centre for Mathematics & its Applications, 2014) Bui, The AnhLet (X,μ) be a non-homogeneous space in the sense that X is a metric space equipped with an upper doubling measure μ. The aim of this paper is to study the endpoint estimate of the maximal operator associated to a Calderón-Zygmund operator T and the Lp boundedness of the maximal commutator with RBMO functionsItem Open Access Quadratic estimates for perturbed dirac type operators on doubling measure metric spaces(The Australian National University, Mathematical Sciences Institute, Centre for Mathematics & its Applications, 2011-02) Bandara, LashiWe consider perturbations of Dirac type operators on complete, connected metric spaces equipped with a doubling measure. Under a suitable set of assumptions, we prove quadratic estimates for such operators and hence deduce that these operators have a bounded functional calculus. In particular, we deduce a Kato square root type estimate.Item Open Access Lectures on Geometric Measure Theory(The Australian National University, Mathematical Sciences Institute, Centre for Mathematics & its Applications, 1983-01-01) Simon, LeonThese notes grew out of lectures given by the author at the Institut für Angewandte Mathematik, Heidelberg University, and at the Centre for Mathematical Analysis, Australian National Unviersity A central aim was to give the basic ideas of Geometric Measure Theory in a style readily accessible to analysts. I have tried to keep the notes as brief as possible, subject to the constraint of covering the really important and central ideas. There have of course been omissions; in an expanded version of these notes (which I hope to write in the near future), topics which would obviously have a high priority for inclusion are the theory of flat chains, further applications of G.M.T. to geometric variational problems, P.D.E. aspects of the theory, and boundary regularity theory.Item Open Access Integration Structures(The Australian National University, Mathematical Sciences Institute, Centre for Mathematics & its Applications, 1988-08) Kluvánek, IgorThe term "structure" in the title is used in the Bourbakist sense. Chapter 0 is devoted to the exposition of a certain notorious failure, or inadequacy, of currently used integration structures, including those presented in Book 5 of the Bourbaki treatise and in the well-known text of PR Halmos. In Section G of that chapter, the nature of the integration structures presented here is briefly described. This description is amplified somewhat in the pre-ambles to chapters 2, 3 and 4.Item Open Access Harmonic mappings between Riemannian manifolds(The Australian National University, Mathematical Sciences Institute, Centre for Mathematics & its Applications, 1984-01-01) Jost, JurgenThese notes originated from a series of lectures I delivered at the Centre for Mathematical Analysis at Canberra. The purpose of the lectures was to introduce mathematicians familiar with the basic notions and results of linear elliptic partial differential equations and Riemannian geometry to the subject of harmonic mappings. I selected some topics to the presentation of which I felt I could contribute something, while on the other hand it was possible to provide complete and detailed proofs of them during these lectures. Thus, these notes are not meant to cover all that is known about harmonic maps, but nevertheless I believe that they give a good account of many of the interesting aspects of the subject and a fair idea of the variety of techniques used in the field.Item Open Access Basic theory of one-parameter semigroups(The Australian National University, Mathematical Sciences Institute, Centre for Mathematics & its Applications, 1982-07-01) Robinson, Derek W.Continuous one-parameter semigroups of bounded operators occur in many branches of mathematics, both pure and applied. The calculus of functions of one real variable can be formulated in terms of the translation semigroup, solutions of the equations connected with classical phenomena such as heat propagation are described by semigroups, and one-parameter groups and semigroups also describe the dynamics of quantum mechanical systems. Although semigroups occur in many other areas the development and scope of the general theory covered in this chapter is well illustrated by the foregoing examples. Hence we begin with a brief discussion of each of them.