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**A weakly polyhomogeneous calculus for pseudodifferential boundary problems.**
*(English)*
Zbl 0998.58017

Parameter-dependent pseudodifferential operators are used in the study of resolvents of boundary value problems, in the construction of complex powers of operators and of solutions of time-dependent problems.

Extending previous work of the author with R. Seeley on a calculus of weakly parametric pseudodifferential operators on closed manifolds to the case of manifolds with boundary, the author studies weakly polyhomogeneous singular Green operators, Poisson operators, traces operators associated with a manifold with boundary, as well as suitable transmission conditions for pseudodifferential operators. Full composition formulas are established for the calculus, which contain the resolvents of Atiyah-Patodi-Singer-type problems.

Extending previous work of the author with R. Seeley on a calculus of weakly parametric pseudodifferential operators on closed manifolds to the case of manifolds with boundary, the author studies weakly polyhomogeneous singular Green operators, Poisson operators, traces operators associated with a manifold with boundary, as well as suitable transmission conditions for pseudodifferential operators. Full composition formulas are established for the calculus, which contain the resolvents of Atiyah-Patodi-Singer-type problems.

Reviewer: Otto Liess (Bologna)

### MSC:

58J40 | Pseudodifferential and Fourier integral operators on manifolds |

### References:

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