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On the Weierstrass preparation theorem. (English. Russian original) Zbl 0999.32004
Math. Notes 69, No. 2, 170-174 (2001); translation from Mat. Zametki 69, No. 2, 194-199 (2001).
The authors investigate the Weierstrass preparation theorem. They show an effective method for finding the nonvanishing function and the coefficients of the distinguished polynomial in the form of Taylor series. The method is applied to the study of bifurcation diagrams of families of analytic functions.
The authors mention that the results of the paper can be carried over to the case of infinitely differentiable functions and the Malgrange preparation theorem.

MSC:
32B05 Analytic algebras and generalizations, preparation theorems
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