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The Weierstrass Preparation Theorem and Its Consequences

2018 ◽  
pp. 43-104
Author(s):  
José Manuel Aroca ◽  
Heisuke Hironaka ◽  
José Luis Vicente
Keyword(s):  
Weierstrass Preparation ◽  
Preparation Theorem

scholarly journals On the Weierstrass Preparation Theorem with Applications to the Asymptotic Analysis of Characteristics Roots of Time-Delay Systems.

2015 ◽  
Vol 48 (12) ◽  
pp. 251-256 ◽  
Author(s):  
F. Méndez-Barrios ◽  
S.-I. Niculescu ◽  
J. Chen ◽  
V.M. Cárdenas-Galindo
Keyword(s):  
Time Delay ◽  
Asymptotic Analysis ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Weierstrass Preparation ◽  
Preparation Theorem

scholarly journals A Note on the Weierstrass Preparation Theorem in Quasianalytic Local Rings

2014 ◽  
Vol 57 (3) ◽  
pp. 614-620 ◽  
Author(s):  
Adam Parusiński ◽  
Jean-Philippe Rolin
Keyword(s):  
Analytic Functions ◽  
Local Rings ◽  
Smooth Functions ◽  
Implicit Equation ◽  
Weierstrass Preparation ◽  
Preparation Theorem

AbstractConsider quasianalytic local rings of germs of smooth functions closed under composition, implicit equation, and monomial division. We show that if theWeierstrass Preparation Theoremholds in such a ring, then all elements of it are germs of analytic functions.

scholarly journals Fibers of flat morphisms and Weierstrass preparation theorem

2014 ◽  
Vol 411 ◽  
pp. 337-355 ◽  
Author(s):  
Trung Cườ̀ng Đoàn
Keyword(s):  
Weierstrass Preparation ◽  
Preparation Theorem

scholarly journals Failure of the Weierstrass Preparation Theorem in quasi-analytic Denjoy–Carleman rings

2014 ◽  
Vol 258 ◽  
pp. 397-413 ◽  
Author(s):  
Francesca Acquistapace ◽  
Fabrizio Broglia ◽  
Michail Bronshtein ◽  
Andreea Nicoara ◽  
Nahum Zobin
Keyword(s):  
Weierstrass Preparation ◽  
Preparation Theorem

scholarly journals Weierstrass preparation and algebraic invariants

2012 ◽  
Vol 356 (4) ◽  
pp. 1405-1424 ◽  
Author(s):  
David Harbater ◽  
Julia Hartmann ◽  
Daniel Krashen
Keyword(s):  
Algebraic Invariants ◽  
Weierstrass Preparation
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