Functional Equations on Groups

This volume provides an accessible and coherent introduction to some of the scientific progress on functional equations on groups in the last two decades. It presents the latest methods of treating the topic and contains new and transparent proofs. Its scope extends from the classical functional equations on the real line to those on groups, in particular, non-abelian groups. This volume presents, in careful detail, a number of illustrative examples like the cosine equation on the Heisenberg group and on the group SL(2, ℝ). Some of the examples are not even seen in existing monographs. Thus, it is an essential source of reference for further investigations.

Contents:

• Introduction

• Around the Additive Cauchy Equation

• The Multiplicative Cauchy Equation

• Addition and Subtraction Formulas

• Levi–Civita's Functional Equation

• The Symmetrized Sine Addition Formula

• Equations with Symmetric Right Hand Side

• The Pre-d'Alembert Functional Equation

• D'Alembert's Functional Equation

• D'Alembert's Long Functional Equation

• Wilson's Functional Equation

• Jensen's Functional Equation

• The Quadratic Functional Equation

• K-Spherical Functions

• The Sine Functional Equation

• The Cocycle Equation

• Appendices:

  • Basic Terminology and Results
  • Substitutes for Commutativity
  • The Casorati Determinant
  • Regularity
  • Matrix-Coefficients of Representations
  • The Small Dimension Lemma
  • Group Cohomology

Readership: Advanced undergraduates, graduates and professional mathematicians interested in harmonic analysis and/or functional equations.
Key Features:

• Most of the material of the book can be found only in research papers, so it is a good source of reference
• The book is self-contained and provides the necessary background material needed to go further into the subject and to explore the research literature
• The book may be used as a textbook for graduate students and even ambitious undergraduate in mathematics, because it presents the material in an accessible way, originating from a course for students at master's level
• Exercises at the end of each chapter, some with answers, help to provide more examples to enable the student to grasp the topic better