Existence and Continuity of Solutions to a Class of Pseudodifferential Equations overp-Adic Field

摘要

We study the pseudodifferential operatorTαand the pseudodifferential equations of typeTαu+u=δxkoverp-adic fieldℚp, whereδxkis the Dirac delta function. We discuss the existence and uniqueness of solutions to the equations. Furthermore, we give conditions for the continuity of the solutionsukwhenubelongs to the spaceL2(ℚp).