论文标题
函数的全球合理近似值具有分解分歧渐近系
Global Rational Approximations of Functions With Factorially Divergent Asymptotic Series
论文作者
论文摘要
我们构建了一种新型的收敛性和渐近表示形式，二元扩展。它们的收敛是几何，融合区域通常从无穷大降至$ 0^+$。我们表明，二元扩展是数值有效的表示。对于特殊功能，例如Bessel，Airy，EI，Erfc，Gamma等。二元组系列的收敛区域是复杂的平面减去射线，并随意选择此切割。因此，二元扩展提供了均匀的，几何收敛的渐近膨胀，包括近抗动物射线。我们证明，相对一般的功能，écalle复发性具有融合的二元扩展。这些扩展扩展到操作员，从而根据在某些规定的离散时间评估的相关统一进化运算符（或者，对于生成的半群）而言，自助接合运算符的分解为串联。
We construct a new type of convergent, and asymptotic, representations, dyadic expansions. Their convergence is geometric and the region of convergence often extends from infinity down to $0^+$. We show that dyadic expansions are numerically efficient representations. For special functions such as Bessel, Airy, Ei, erfc, Gamma, etc. the region of convergence of dyadic series is the complex plane minus a ray, with this cut chosen at will. Dyadic expansions thus provide uniform, geometrically convergent asymptotic expansions including near antistokes rays. We prove that relatively general functions, Écalle resurgent ones, possess convergent dyadic expansions. These expansions extend to operators, resulting in representations of the resolvent of self-adjoint operators as series in terms of the associated unitary evolution operator evaluated at some prescribed discrete times (alternatively, for positive operators, in terms of the generated semigroup).
