This Proceedings contains a collection of articles by front-line researchers in Mathematical Analysis, giving the reader a wide perspective of the current research in several areas like Functional Analysis, Complex Analysis and Measure Theory. The works are a fundamental source for current and future developments in these research fields. The articles and surveys have been collected as well as reference results scattered in the corresponding literature and thus, are highly useful to researchers.

Basic Analysis IV: Measure Theory and Integration introduces students to concepts from measure theory and continues their training in the abstract way of looking at the world. This is a most important skill to have when your life's work will involve quantitative modeling to gain insight into the real world. This text generalizes the notion of integration to a very abstract setting in a variety of ways. We generalize the notion of the length of an interval to the measure of a set and learn how to construct the usual ideas from integration using measures. We discuss carefully the many notions of convergence that measure theory provides. Features • Can be used as a traditional textbook as well as for self-study • Suitable for advanced students in mathematics and associated disciplines • Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions

This volume is dedicated to the memory of Sergey Naboko (1950-2020). In addition to original research contributions covering the vast areas of interest of Sergey Naboko, it includes personal reminiscences and comments on the works and legacy of Sergey Naboko’s scientific achievements. Areas from complex analysis to operator theory, especially, spectral theory, are covered, and the papers will inspire current and future researchers in these areas.

Authored by a ranking authority in Gaussian harmonic analysis, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: harmonic analysis and probability. The book is intended for a very diverse audience, from graduate students all the way to researchers working in a broad spectrum of areas in analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of real analysis as well as with classical harmonic analysis, including Calderón-Zygmund theory; also some knowledge of basic orthogonal polynomials theory would be convenient. The monograph develops the main topics of classical harmonic analysis (semigroups, covering lemmas, maximal functions, Littlewood-Paley functions, spectral multipliers, fractional integrals and fractional derivatives, singular integrals) with respect to the Gaussian measure. The text provide an updated exposition, as self-contained as possible, of all the topics in Gaussian harmonic analysis that up to now are mostly scattered in research papers and sections of books; also an exhaustive bibliography for further reading. Each chapter ends with a section of notes and further results where connections between Gaussian harmonic analysis and other connected fields, points of view and alternative techniques are given. Mathematicians and researchers in several areas will find the breadth and depth of the treatment of the subject highly useful.

This report uses data from the National Longitudinal Study of the High School Class of 1972 and the High School & Beyond/Sophomores Study to summarize information on what is studied, where, and by whom, in the nation's colleges, community colleges, and postsecondary trade schools. Section 1 describes how the data is based on that which the taxonomy of courses and analyses of course-taking, credits, grades, degrees, etc., were constructed and edited. Section 2, "Degrees, Majors, Credits, and Time," presents the long-term educational attainment of the two cohorts of students (classes of 1972 and 1982). Section 3, "The Changing Shape of Delivered Knowledge," presents the taxonomy of courses, and includes the most common course titles in over 1,000 course categories, as well as enrollment trends by course category. Section 4 examines all credits earned by the two cohorts and identifies which courses account for most of those credits to yield an empirical "core curriculum." Section 5 provides data on proportions of students studying given subject categories; trend data is included for the past two decades. Finally, Section 6 provides data concerning such issues as trends in grade inflation and which courses students fail at high rates. The conclusion offers suggestions for further analysis of these data bases. (Contains 43 references.) (DB)