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The Superstability of the Generalized D'alembert Functional Equation
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Elhoucien Elqorachi
Published/Copyright:
March 10, 2010
Abstract
We generalize the well-known Baker's superstability result for the d'Alembert functional equation with values in the field of complex numbers to the case of the integral equation
where 𝐺 is a locally compact group, μ is a generalized Gelfand measure and σ is a continuous involution of 𝐺.
Key words and phrases:: D'Alembert equation; Gelfand measure; Gelfand pair; stability; superstability
Received: 2002-03-18
Revised: 2002-09-24
Published Online: 2010-03-10
Published in Print: 2003-September
© Heldermann Verlag
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- On the Mathematical Basis of the Linear Sampling Method
- Solvability and Asymptotics of Solutions of Crack-Type Boundary-Contact Problems of the Couple-Stress Elasticity
- Integral Representations for the Solution of Dynamic Bending of a Plate with Displacement-Traction Boundary Data
- Laguerre-Type Exponentials, and the Relevant 𝐿-Circular and 𝐿-Hyperbolic Functions
- About Asymptotic and Oscillation Properties of the Dirichlet Problem for Delay Partial Differential Equations
- The Superstability of the Generalized D'alembert Functional Equation
- First Order Partial Functional Differential Equations with Unbounded Delay
- The Dirichlet Problem for Harmonic Functions with Boundary Values from Zygmund Classes
- On the Asymptotics of Solutions of Elliptic Equations in a Neighborhood of a Crack with Nonsmooth Front
- A Factorization Method for an Inverse Neumann Problem for Harmonic Vector Fields
- A Bound for Reflections Across Jordan Curves
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Keywords for this article
D'Alembert equation;
Gelfand measure;
Gelfand pair;
stability;
superstability
Articles in the same Issue
- On Fourier Series in Eigenfunctions of Elliptic Boundary Value Problems
- On the Mathematical Basis of the Linear Sampling Method
- Solvability and Asymptotics of Solutions of Crack-Type Boundary-Contact Problems of the Couple-Stress Elasticity
- Integral Representations for the Solution of Dynamic Bending of a Plate with Displacement-Traction Boundary Data
- Laguerre-Type Exponentials, and the Relevant 𝐿-Circular and 𝐿-Hyperbolic Functions
- About Asymptotic and Oscillation Properties of the Dirichlet Problem for Delay Partial Differential Equations
- The Superstability of the Generalized D'alembert Functional Equation
- First Order Partial Functional Differential Equations with Unbounded Delay
- The Dirichlet Problem for Harmonic Functions with Boundary Values from Zygmund Classes
- On the Asymptotics of Solutions of Elliptic Equations in a Neighborhood of a Crack with Nonsmooth Front
- A Factorization Method for an Inverse Neumann Problem for Harmonic Vector Fields
- A Bound for Reflections Across Jordan Curves
- A Direct Method for Boundary Integral Equations on a Contour with a Peak
- On Two-Point Boundary Value Problems for Two-Dimensional Differential Systems with Singularities
