Borel summability of the unequal double well

Transseries and Écalle-Borel summability

Topological Construction of Transseries and Introduction to Generalized Borel Summability

Transseries in the sense of Écalle are constructed using a topological approach. A general contractive mapping principle is formulated and proved, showing the closure of transseries under a wide class of operations. In the second part we give an overview of results and methods reconstruction of actual functions and solutions of equations from transseries by generalized Borel summation with in o...

: Existence and Uniqueness of Solutions , Asymptotic and Borel Summability Properties

We consider a system of n-th order nonlinear quasilinear partial differential equations of the form ut + P(∂ j x)u + g ( x, t, {∂ xu} ) = 0; u(x, 0) = uI(x) with u ∈ C, for t ∈ (0, T ) and large |x| in a poly-sector S in C (∂ x ≡ ∂ j1 x1∂ j2 x2 ...∂ jd xd and j1 + ... + jd ≤ n). The principal part of the constant coefficient n-th order differential operator P is subject to a cone condition. The...

On Summability of Double Series*

On a High-indices Theorem in Borel Summability

I K. KNOPP, Über das Eulersche Summierungsverfahren . 1, Math . Zeitschr., 15 (1922), pp. 226-253 ; 11, 18 (1923), pp. 125-156. -' W. MEYER-KÖNIG, Die Umkehrung des Euler-Knoppschen and des Borelschen Limitierungsverfahrens auf Grund einer Luckenbedingung, Math. Zeitschr ., 49 (1943-44), pp. 151-160 . 3 P. ERDÖS, Acad. Serbe Sci. Publ. Inst. Math ., 4 (1952), pp . 51-56. Recently MEYERKÖNIG pro...