Oscillatory Integrals and Restriction
Stationary phase, Stein–Tomas restriction, and decoupling theorems.
Oscillatory Integrals and Restriction. Stationary phase, Stein–Tomas restriction, and decoupling theorems.
Foundations and canonical references
The standard treatments of oscillatory integrals and restriction approach the subject from complementary angles. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals (1993) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Open methodological questions for oscillatory integrals and restriction include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1993Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integralsstein-1993
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