 Conic support of an oscillatory amplitude

A closed conic enlargement of an oscillatory integral amplitude support is obtained by taking the closure of its frequency-direction projection in $X\times S^{k-1}$ and lifting that set radially to nonzero frequencies. It records limiting spatial locations and frequency directions, including limits reached only at arbitrarily large frequency. Ordinary support in $X\times {\mathbb{R}}^k$ need not record those limits. This distinction is necessary in singular support bounds for an oscillatory integral.