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

الملخص EN

We study the pseudodifferential operator Tα and the pseudodifferential equations of type Tαu+u=δxk over p-adic field ℚp, where δxk is the Dirac delta function.

We discuss the existence and uniqueness of solutions to the equations.

Furthermore, we give conditions for the continuity of the solutions uk when u belongs to the space L2(ℚp).