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En 1993, Mark A. Pinsky dio a conocer un comportamiento inesperado de la transformada de Fourier para funciones suaves a trozos definidas en el espacio real ndimensional. Conociendo la transformada de Fourier, un problema fundamental del Anlisis de Fourier es el de su inversin puntual, el cual consiste en hallar la funcin, en puntos determinados, de la cual proviene esa transformada. Es un resultado conocido en esta rea de las matemticas que este problema es resuelto para funciones suaves a trozos definidas en el espacio real. El fenmeno hallado por Pinsky consisti en probar que existan funciones suaves a trozos definidas en el espacio real ndimensional, donde n es mayor o igual a tres, para las cuales no se tena un comportamiento similar. En este texto explicamos en detalle el fenmeno de Pinsky y mostramos que el problema de inversin puntual para la transformada de Fourier se resuelve para funciones suaves definidas sobre cuerpos convexos que estn en posicin general con el dominio conexo sobre el que se considera el operador suma parcial. Si estos cuerpos estn conectados Legendre, entonces no se cumple la inversin en el origen.
⚠️ WARNING (California Proposition 65):
This product may contain chemicals known to the State of California to cause cancer,
birth defects, or other reproductive harm.
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