Palabras clave
conjuntos estructurales
funciones inframogénicas
operador de dirac
Cómo citar
Resumen
El análisis de Clifford se enfoca en las llamadas funciones monogénicas, reconocidas como generalizaciones naturales de las funciones holomorfas del plano complejo. Debido a la no conmutatividad del producto en álgebras de Clifford, surgen las funciones inframonogénicas como versión no conmutativa de las funciones armónicas. La construcción de operadores de Dirac con bases ortonormales arbitrarias de ℝᵐ posibilita el surgimiento de una nueva subclase de funciones biarmónicas que generalizan a las funciones inframonogénicas. En este trabajo se tratará la fórmula integral de Cauchy y un problema de salto para este tipo de funciones, así como la conexión con el sistema de Lamé-Navier. Al finalizar se mostrarán problemas de frontera bien planteados y descomposiciones de Fischer para el espacio de polinomios ℝᵐ[x].
Referencias
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