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Some gap power series in multidimensional setting

100%

Siciak J.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2011

tom 65

nr 2

We study extensions of classical theorems on gap power series of a complex variable to the multidimensional case.

Convergence of power series along vector fields and their commutators; a Cartan-Kähler type theorem

86%

Jakubczyk B.

Annales Polonici Mathematici

2000

tom 74

nr 1

117-132

We study convergence of formal power series along families of formal or analytic vector fields. One of our results says that if a formal power series converges along a family of vector fields, then it also converges along their commutators. Using this theorem and a result of T. Morimoto, we prove analyticity of formal solutions for a class of nonlinear singular PDEs. In the proofs we use results from control theory.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

1 Jakubczyk B.

1 Siciak J.

1 2011

1 2000

Wyniki wyszukiwania

Some gap power series in multidimensional setting

Convergence of power series along vector fields and their commutators; a Cartan-Kähler type theorem