Asymptotic Behaviour Of Tame Harmonic Bundles And An Application To Pure Twistor D Modules Part 1
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Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 1
Author: Takuro Mochizuki
language: en
Publisher: American Mathematical Soc.
Release Date: 2007
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.
Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 2
Author: Takuro Mochizuki
language: en
Publisher: American Mathematical Soc.
Release Date: 2007
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 regularholonomic $D$-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.
Asymptotic Expansions for Infinite Weighted Convolutions of Heavy Tail Distributions and Applications
Author: Philippe Barbe
language: en
Publisher: American Mathematical Soc.
Release Date: 2009
"January 2009, volume 197, number 922 (Fourth of five numbers)."