Abstract:
In this paper, we prove the general invertibility theorem for
non-local pseudo-differential operators and using this, we establish
the theorems of analytic continuation and of existence
of holomorphic solutions to non-local differential equations.
We also obtain a concrete method to construct a holomorphic solutions to
constant coefficient equations.
Key Words: Pseudo-differential operators,
partial differential equations of infinite ordre, non-local equations,
differential-difference equations.
2000 Mathematics Subject Classification: Primary:
35S99;
Secondary: 35R50, 35A27.
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