Stephan Ramon Garcia

William T. Ross

Javad Mashreghi

The study of model spaces, the closed invariant subspaces of the backward shift operator, is a vast area of research with connections to complex analysis, operator theory and functional analysis. This self-contained text is the ideal introduction for newcomers to the field. It sets out the basic ideas and quickly takes the reader through the history of the subject before ending up at the frontier of mathematical analysis. Open questions point to potential areas of future research, offering plenty of inspiration to graduate students wishing to advance further.

Introduction to Model Spaces and their Operators

Voice Culture and Elocution

Alexandru Aleman

Nathan S. Feldman

If H is a Hilbert space and T : H ? H is a continous linear operator, a natural question to ask is: What are the closed subspaces M of H for which T M ? M? Of course the famous invariant subspace problem asks whether or not T has any non-trivial invariant subspaces. This monograph is part of a long line of study of the invariant subspaces of the operator T = M (multiplication by the independent variable z, i. e. , M f = zf )on a z z Hilbert space of analytic functions on a bounded domain G in C. The characterization of these M -invariant subspaces is particularly interesting since it entails both the properties z of the functions inside the domain G, their zero sets for example, as well as the behavior of the functions near the boundary of G. The operator M is not only interesting in its z own right but often serves as a model operator for certain classes of linear operators. By this we mean that given an operator T on H with certain properties (certain subnormal operators or two-isometric operators with the right spectral properties, etc. ), there is a Hilbert space of analytic functions on a domain G for which T is unitarity equivalent to M .

The Hardy Space of a Slit Domain

In 1919, the novelist H. G. Wells published the first edition of The Outline of History, a work destined to be one of the enduring cultural documents of the twentieth century. Aimed at the general reader, the 500,000-word effort was intended by Wells to provide the necessary background so that educated citizens (from any part of the globe) could start to discard their nationalistic and theological blinders and start to see the world as it really was. To Wells's way of thinking, the only way to prevent disasters like World War I, which had just ended, was to drop outmoded prejudices altogether and create a one-world government. The work was an immense success, selling over two million copies in various editions and translations in its first ten years. It was especially popular in the United States, staying in print until the 1970s. In the first extended study of these works, Ross analyzes them as products of a progressive mindset convinced that the Enlightenment tradition of science and reason was the perfect antidote to the current disastrous situation. In addition to asking how far Wells's rhetoric and organization allow his reformist aims to be realized in the Outline, Ross also interrogates all three works on a number of critical topics to see how well Wells's views hold up against contemporary attitudes.

The Outline of History and Its Companions

H.G. Wells's World Reborn

Joseph A. Cima

Alec L. Matheson

The Cauchy transform of a measure on the circle is a subject of both classical and current interest with a sizable literature. This book is a thorough, well-documented, and readable survey of this literature and includes full proofs of the main results of the subject. This book also covers more recent perturbation theory as covered by Clark, Poltoratski, and Aleksandrov and contains an indepth treatment of Clark measures.

The Cauchy Transform

Weldon Kees

Catherine Bénéteau:

Alberto A. Condori

Constanze Liaw

Alan A. Sola

This volume contains the Proceedings of the Conference on Completeness Problems, Carleson Measures, and Spaces of Analytic Functions, held from June 29–July 3, 2015, at the Institut Mittag-Leffler, Djursholm, Sweden. The conference brought together experienced researchers and promising young mathematicians from many countries to discuss recent progress made in function theory, model spaces, completeness problems, and Carleson measures. This volume contains articles covering cutting-edge research questions, as well as longer survey papers and a report on the problem session that contains a collection of attractive open problems in complex and harmonic analysis.

William T. Ross

Books

Your next favorite book is out there