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Pseudo-differential operators of infinite order on and applications to the cauchy problem for some elementary operators

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Lo scopo di questo lavoro è quello di provare delle condizioni sufficienti affinchè, per una certa classe di operatori, ci sia buona positura del problema di Cauchy anche in certi spazi il cui indice di Gevrey è maggiore del massimo indice «ammissibile» noto dalla letteratura. Le tecniche usate sono quelle della costruzione di una parametrice tramite la risoluzione delle equazioni del trasporto; a tale scopo nella prima parte del lavoro viene sviluppato un calcolo per gli operatori pseudodifferenziali di ordine infinito negli spazi presi in considerazione.

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Agliardi, R. Pseudo-differential operators of infinite order on and applications to the cauchy problem for some elementary operators. Annali di Matematica pura ed applicata 157, 369–394 (1990). https://doi.org/10.1007/BF01765323

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