Jae-Hyun Yang

Generalized Heisenberg Groups and the Schrödinger–Weil Representation

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This monograph provides a detailed study of generalized Heisenberg groups, which are 2-step nilpotent Lie groups appearing naturally in the theory of Siegel modular varieties, automorphic forms, number theory, and mathematical physics. The author develops the theory systematically and explains how these groups are connected with theta functions, the Weil representation, and the Schrödinger–Weil representation.

The book emphasizes both the algebraic structure and representation-theoretic aspects of generalized Heisenberg groups. It aims to provide explicit constructions and conceptual explanations that help readers understand the interplay among harmonic analysis, automorphic forms, and mathematical physics.

The text is intended for:

TABLE OF CONTENTS

Chapter 1. Generalized Heisenberg Groups

Chapter 2. The Schrödinger–Weil Representation

This book provides a concise but specialized treatment of the subject, focusing on the deep relationship between generalized Heisenberg groups, theta functions, and the Schrödinger–Weil representation.

Edited by Daniel Alpay, Fabrizio Colombo, and Irene Sabadini

Operator Theory (Second Edition)

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Operator Theory is a comprehensive reference work covering modern developments in operator theory and its applications. The subject concerns the study of linear continuous operators acting on topological vector spaces such as Banach spaces, Hilbert spaces, and Fréchet spaces. The field connects deeply with functional analysis, complex analysis, mathematical physics, engineering, signal processing, machine learning, and quantum theory.

The editors assembled contributions from leading researchers to reflect both classical foundations and emerging areas of research. Special emphasis is placed on interactions between operator theory and related disciplines such as hypercomplex analysis, free probability, reproducing kernel Hilbert spaces, system theory, and non-commutative mathematics.

The work is intended for:

TABLE OF CONTENTS

The major thematic sections include:

  1. General Aspects of Quaternionic and Clifford Analysis
  2. Further Developments of Quaternionic and Clifford Analysis
  3. Infinite Dimensional Analysis
  4. Non-Commutative Theory
  5. Multivariable Operator Theory
  6. Reproducing Kernel Hilbert Spaces
  7. de Branges Spaces
  8. Indefinite Inner Product Spaces
  9. Schur Analysis
  10. Linear System Theory

Additional editorial and research topics covered throughout the volumes include:

This edition serves as a large-scale reference encyclopedia on contemporary operator theory, bringing together survey articles and research-oriented chapters from experts across many areas of mathematics.

Samuel Nascimento de Araújo, Nicolas de Almeida Martins, Nicolas Nisse, and Rudini M. Sampaio

Theory of Combinatorial Games in Graphs

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This textbook provides a modern introduction to combinatorial game theory with a special emphasis on games played on graphs. It is intended primarily for advanced undergraduate students, while also serving as a useful reference for graduate students and researchers interested in graph theory, algorithms, and game theory.

The book develops the fundamental mathematical theory of combinatorial games and then applies it to a wide variety of graph-based games. Topics include impartial and partisan games, positional games, computational complexity, graph coloring games, connectivity games, domination games, convexity games, and pursuit–evasion games such as cops-and-robber games.

A notable feature of the book is that it gathers several active research topics that are usually scattered across research papers and presents them in a unified and accessible framework. Readers are introduced not only to classical results such as the Sprague–Grundy theory but also to contemporary developments at the intersection of graph theory and combinatorial game theory.

TABLE OF CONTENTS

The book is organized into three major parts:

Part I – Foundations of Combinatorial Game Theory

Part II – Games on Graphs

Part III – Theory of Partizan Games

MATHEMATICAL TOPICS COVERED

This book serves as both an introduction and a bridge to current research, making it particularly valuable for students and researchers interested in the interaction between combinatorics, graph theory, and strategic games.

Janis E. Johnston, Kenneth J. Berry, and Michael A. Long

Permutation Statistical Methods: Measures of Relationship

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This book provides a concise introduction to measures of relationship used in statistical analysis and emphasizes permutation statistical methods based on the Fisher–Pitman model. The authors present permutation approaches alongside conventional statistical procedures based on the Neyman–Pearson framework, allowing readers to compare the two methodologies directly.

The text covers a broad range of association measures, including:

A major goal of the book is to demonstrate how permutation methods can provide alternative significance assessments and inferential procedures that are often less dependent on classical distributional assumptions. Numerous examples illustrate the differences between permutation-based and conventional probability values.

The volume serves as a companion to the authors' earlier work, Permutation Statistical Methods: Tests of Differences, extending the permutation framework from hypothesis testing to the analysis of relationships among variables.

TABLE OF CONTENTS

Chapter 1. Introduction

Chapter 2. Permutation Statistical Methods

Chapter 3. Measures of Nominal Association

Chapter 4. Measures of Ordinal Association

Chapter 5. Measures of Correlation

Chapter 6. Mixed Measures of Association

ABOUT THE AUTHORS