Daniele C. Struppa

Irene Sabadini

Fabrizio Colombo

Franciscus Sommen

* The main treatment is devoted to the analysis of systems of linear partial differential equations (PDEs) with constant coefficients, focusing attention on null solutions of Dirac systems * All the necessary classical material is initially presented * Geared toward graduate students and researchers in (hyper)complex analysis, Clifford analysis, systems of PDEs with constant coefficients, and mathematical physics

Analysis of Dirac Systems and Computational Algebra

Leon Ehrenpreis has been one of the leading mathematicians in the twentieth century. His contributions to the theory of partial differential equations were part of the golden era of PDEs, and led him to what is maybe his most important contribution, the Fundamental Principle, which he announced in 1960, and fully demonstrated in 1970. His most recent work, on the other hand, focused on a novel and far reaching understanding of the Radon transform, and offered new insights in integral geometry. Leon Ehrenpreis died in 2010, and this volume collects writings in his honor by a cadre of distinguished mathematicians, many of which were his collaborators.

The Mathematical Legacy of Leon Ehrenpreis

Daniel Alpay

Jussi Behrndt

This book features a collection of papers by plenary, semi-plenary and invited contributors at IWOTA2021, held at Chapman University in hybrid format in August 2021. The topics span areas of current research in operator theory, mathematical physics, and complex analysis.

IWOTA 2021, Chapman University

Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis

Michael Shapiro

Maria Elena Luna-Elizarrarás

This book provides the foundations for a rigorous theory of functional analysis with bicomplex scalars. It begins with a detailed study of bicomplex and hyperbolic numbers and then defines the notion of bicomplex modules. After introducing a number of norms and inner products on such modules (some of which appear in this volume for the first time), the authors develop the theory of linear functionals and linear operators on bicomplex modules. All of this may serve for many different developments, just like the usual functional analysis with complex scalars and in this book it serves as the foundational material for the construction and study of a bicomplex version of the well known Schur analysis.

Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis

Yakir Aharonov

Jeff Tollaksen

In the past 50 years, quantum physicists have discovered, and experimentally demonstrated, a phenomenon which they termed superoscillations. Aharonov and his collaborators showed that superoscillations naturally arise when dealing with weak values, a notion that provides a fundamentally different way to regard measurements in quantum physics. From a mathematical point of view, superoscillating functions are a superposition of small Fourier components with a bounded Fourier spectrum, which result, when appropriately summed, in a shift that can be arbitrarily large, and well outside the spectrum. The purpose of this work is twofold: on one hand the authors provide a self-contained survey of the existing literature, in order to offer a systematic mathematical approach to superoscillations; on the other hand, they obtain some new and unexpected results, by showing that superoscillating sequences can be seen of as solutions to a large class of convolution equations and can therefore be treated within the theory of analytically uniform spaces. In particular, the authors will also discuss the persistence of the superoscillatory behavior when superoscillating sequences are taken as initial values of the Schrödinger equation and other equations.

The Mathematics of Superoscillations

Mihaela B. Vajiac

This book gathers contributions written by Daniel Alpay’s friends and collaborators. Several of the papers were presented at the International Conference on Complex Analysis and Operator Theory held in honor of Professor Alpay’s 60th birthday at Chapman University in November 2016. The main topics covered are complex analysis, operator theory and other areas of mathematics close to Alpay’s primary research interests. The book is recommended for mathematicians from the graduate level on, working in various areas of mathematical analysis, operator theory, infinite dimensional analysis, linear systems, and stochastic processes.

Festschrift in Honor of Daniel Alpay’s 60th Birthday

Advances in Complex Analysis and Operator Theory

Douglas R. Dechow

This engaging volume celebrates the life and work of Theodor Holm “Ted” Nelson, a pioneer and legendary figure from the history of early computing. Presenting contributions from world-renowned computer scientists and figures from the media industry, the book delves into hypertext, the docuverse, Xanadu and other products of Ted Nelson’s unique mind. Features: includes a cartoon and a sequence of poems created in Nelson’s honor, reflecting his wide-ranging and interdisciplinary intellect; presents peer histories, providing a sense of the milieu that resulted from Nelson’s ideas; contains personal accounts revealing what it is like to collaborate directly with Nelson; describes Nelson’s legacy from the perspective of his contemporaries from the computing world; provides a contribution from Ted Nelson himself. With a broad appeal spanning computer scientists, science historians and the general reader, this inspiring collection reveals the continuing influence of the original visionary of the World Wide Web.

Daniele C. Struppa

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