Scholarlink

<p>We describe an elementary method for bounding a one-dimensional oscillatory integral in terms of an associated non-oscillatory integral. The bounds obtained are efficient in an appropriate sense and behave well under perturbations of the phase. As a consequence, for an <i>n</i>-dimensional oscillatory integral with a critical point at the origin, we may apply the one-dimensional estimates in the radial direction and then integrate the result, thereby obtaining a natural bound for the <i>n</i>-dimensional oscillatory integral in terms of an analogous associated non-oscillatory integral. To illustrate, we provide several classes of examples, including situations where the phase function has a critical point at which it vanishes to infinite order.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A Method for Bounding Oscillatory Integrals in Terms of Non-oscillatory Integrals

  • 期刊论文

  • 发表日期：

    2025年3月18日

查看全文
  • Michael Greenblatt

摘要

We describe an elementary method for bounding a one-dimensional oscillatory integral in terms of an associated non-oscillatory integral. The bounds obtained are efficient in an appropriate sense and behave well under perturbations of the phase. As a consequence, for an n-dimensional oscillatory integral with a critical point at the origin, we may apply the one-dimensional estimates in the radial direction and then integrate the result, thereby obtaining a natural bound for the n-dimensional oscillatory integral in terms of an analogous associated non-oscillatory integral. To illustrate, we provide several classes of examples, including situations where the phase function has a critical point at which it vanishes to infinite order.