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:- Solutions for previously insoluble problems
- Nontrivial behavior for scalar fields
- Novel quantization procedures
