By Norman Bleistein

ISBN-10: 0486650820

ISBN-13: 9780486650821

**Read or Download Asymptotic Expansions of Integrals PDF**

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**Sample text**

Granted this, which will also be proved later, one notes that Q induces an injection Q of the space X into cm; it follows in particular that Q is light at every point of C"'. It will also be seen below that the ring P of polynomials inn variables is integral over pr, hence Q is a proper mapping. Therefore, by [44a: Corollary, p. 87], Q(X) is an analytic subset of C"', and as such is a complex analytic space, of which the underlying space is homeomorphic to X. (In this case, since only polynomials are involved, a direct, purely algebraic proof of the same fact can be given, not using the analytical results of [44a], cf.

Suppose K(z) =F 0 for every z e D. p(Z) = --_ - log K(z). ,,=o

5Yt)c'Jl. 5Yt to T 0 T Since infinitely many elements of the sequence. 5Yt. 5Yt' of b0 such that T""T0• 00 , 00 00 00 00 00 • 00 30 HOLOMORPHIC FUNCTIONS AND MAPPINGS ON A BOUNDED DOMAIN is defined and equal to the identity there. It now remains to prove that the ranges of T 0 and of T lie in D. We treat the case of T""" Let beD and let B be a compact neighborhood of b, B=BcD. The compositum T 1- 1 Tm is defined for all l and m. We claim that T 1- 1T,. converges weakly to the identity on D. We consider {T1- 1 Tm-id.

### Asymptotic Expansions of Integrals by Norman Bleistein

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