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Fundamental solutions for hypoelliptic differential operators depending analytically on a parameter. (English) Zbl 0785.35008
Summary: Let \(P(\lambda,D)=\sum_{| \alpha | \leq m} a_ \alpha (\lambda) D^ \alpha\) be a differential operator with constant coefficients \(a_ \alpha\) depending analytically on a parameter \(\lambda\). Assume that each \(P(\lambda,D)\) is hypoelliptic and that the strength of \(P(\lambda,D)\) is independent of \(\lambda\). Under this condition we show that there exists a regular fundamental solution of \(P(\lambda,D)\) which also depends analytically on \(\lambda\).

MSC:
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35E05 Fundamental solutions to PDEs and systems of PDEs with constant coefficients
65H10 Numerical computation of solutions to systems of equations
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