The Asymptotic Analysis of Multidimensional Fourier Integrals - An Alternative Derivation.
DENVER RESEARCH INST COLO DIV OF MATHEMATICAL SCIENCES
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The method of multidimensional stationary phase is derived via a technique which makes strong use of integration by parts. The diagonalization of the matrix of second derivatives at the stationary point is carried out here in such a manner as to make all coefficients in the exponent plus or minus 1. This modification of existing technique allows for the explicit calculation of the nth term of the asymptotic expansion in a closed form which involves the amplitude of the integrand in transformed coordinates. The first correction term in the multi-dimensional stationary phase formula is readily calculated from this result. Author
- Theoretical Mathematics