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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Joint continuity of division of smooth functions. I. Uniform Lojasiewicz estimates
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by Mark Alan Mostow and Steven Shnider PDF
Trans. Amer. Math. Soc. 292 (1985), 573-583 Request permission

Abstract:

In this paper we study the question of the existence of a continuous inverse to the multiplication mapping $(f,g) \to (fg,g)$ defined on pairs of ${C^\infty }$ functions on a manifold $M$. Obviously, restrictions must be imposed on the domain of such an inverse. This leads us to the study of a modified problem: Find an appropriate domain for the inverse of $(f,G) \to (f(p \circ G),G)$, where $G$ is a ${C^\infty }$ mapping of the manifold $M$ into an analytic manifold $N$ and $p$ is a fixed analytic function on $N$. We prove a theorem adequate for application to the study of inverting the mapping $(A,X) \to (A,AX)$, where $X$ is a vector valued ${C^\infty }$ function and $A$ is a square matrix valued ${C^\infty }$ function on $M$ whose determinant may vanish on a nowhere dense set.
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 292 (1985), 573-583
  • MSC: Primary 58C25; Secondary 26E10
  • DOI: https://doi.org/10.1090/S0002-9947-1985-0808738-5
  • MathSciNet review: 808738