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On solutions of real analytic equations

Authors:	Tejinder S Neelon

Institution:	College of Arts and Sciences, California State University San Marcos, San Marcos, California 92096

Abstract:	Analyticity of ${\c C}^{\infty }$ solutions $y_i =f_i(x), 1\le i\le m$ , of systems of real analytic equations $p_j(x,y)= 0, 1\le j\le l$ , is studied. Sufficient conditions for ${\c C}^{\infty }$ and power series solutions to be real analytic are given in terms of iterative Jacobian ideals of the analytic ideal generated by $p_1,p_2,\ldots ,p_l$ . In a special case when the 's are independent of , we prove that if a ${\c C}^{\infty }$ solution satisfies the condition $\det \left( \frac {\partial p_i}{py_j}\right )(h(x)) \not \equiv 0$ , then is necessarily real analytic.

Keywords:	Power series rings real analytic equations semianalytic sets

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