标题： 关于Cowling近似：通过泛函和渐近分析方法对假设的验证 显示英文标题

标题： On the Cowling Approximation: A Verification of Ansatz via Methods of Functional and Asymptotic Analysis

摘要： 我们通过解析方法研究Cowling近似，该近似应用于从非径向恒星脉动模型中产生的线性微分方程组。 我们考虑各种渐近情况，包括高谐波阶数和高振荡频率的情况。 我们的方法涉及将该方程组重新表述为一个积分微分方程，其中某些希尔伯特空间方法适用。 通过更全面的渐近研究，我们将结果扩展到某些基本解集，这些解集根据某些多点边值问题进行表征：这种渐近分析进一步使我们能够产生精确的估计，以确认我们的普遍结果。 显示英文摘要

摘要： We study the Cowling approximation by analytical means as applied to a system of linear differential equations arising from models of non-radial stellar pulsation. We consider various asymptotic cases, including those of high harmonic degree and high oscillation frequency. Our methods involve a reformulation of the system in terms of an integro-differential equation for which certain Hilbert-space methods apply. By way of a more complete asymptotic study, we extend our results to certain fundamental solution sets, characterized according to certain multi-point boundary-value problems: Such asymptotics further enable us to produce sharp estimates as confirmation of our general results.