Memoirs of the American Mathematical Society 2007; 324 pp; softcover Volume: 185 ISBN10: 082183942X ISBN13: 9780821839423 List Price: US$88 Individual Members: US$52.80 Institutional Members: US$70.40 Order Code: MEMO/185/869
 The author studies the asymptotic behaviour of tame harmonic bundles. First he proves a local freeness of the prolongment of deformed holomorphic bundle by an increasing order. Then he obtains the polarized mixed twistor structure from the data on the divisors. As one of the applications, he obtains the norm estimate of holomorphic or flat sections by weight filtrations of the monodromies. As another application, the author establishes the correspondence of semisimple regular holonomic \(D\)modules and polarizable pure imaginary pure twistor \(D\)modules through tame pure imaginary harmonic bundles, which is a conjecture of C. Sabbah. Then the regular holonomic version of M. Kashiwara's conjecture follows from the results of Sabbah and the author. Table of Contents Part 1. Preliminary  Preliminary
 Preliminary for mixed twistor structure
 Preliminary for filtrations
 Some lemmas for generically splitted case
 Model bundles
Part 2. Prolongation of Deformed Holomorphic Bundles  Harmonic bundles on a punctured disc
 Harmonic bundles on a product of punctured discs
 The KMSstructure of the space of the multivalued flat sections
 The induced regular \(\lambda\)connection on \(\Delta^n\times C^\ast\)
Part 3. Limiting Mixed Twistor theorem and Some Consequence  The induced vector bundle over \(\mathbb{P}^1\)
 Limiting mixed twistor theorem
 Norm estimate
 Bibliography
 Index
