Displaying similar documents to “The solution of Kato's conjecture (after Auscher, Hofmann, Lacey, McIntosh and Tchamitchian)”

On wild ramification in quaternion extensions

G. Griffith Elder, Jeffrey J. Hooper (2007)

Journal de Théorie des Nombres de Bordeaux

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This paper provides a complete catalog of the break numbers that occur in the ramification filtration of fully and thus wildly ramified quaternion extensions of dyadic number fields which contain - 1 (along with some partial results for the more general case). This catalog depends upon the , which as defined in [] is associated with the biquadratic subfield. Moreover we find that quaternion counter-examples to the conclusion of the Hasse-Arf Theorem are extremely rare and can occur only...

Solution of Cubic and Quartic Equations

Marco Riccardi (2009)

Formalized Mathematics

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In this article, the principal n-th root of a complex number is defined, the Vieta's formulas for polynomial equations of degree 2, 3 and 4 are formalized. The solution of quadratic equations, the Cardan's solution of cubic equations and the Descartes-Euler solution of quartic equations in terms of their complex coefficients are also presented [5].

Klein-Gordon type decay rates for wave equations with time-dependent coefficients

Michael Reissig, Karen Yagdjian (2000)

Banach Center Publications

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This work is concerned with the proof of L p - L q decay estimates for solutions of the Cauchy problem for the Klein-Gordon type equation u t t - λ 2 ( t ) b 2 ( t ) ( Δ u - m 2 u ) = 0 . The coefficient consists of an increasing smooth function λ and an oscillating smooth and bounded function b which are uniformly separated from zero. Moreover, m 2 is a positive constant. We study under which assumptions for λ and b one can expect as an essential part of the decay rate the classical Klein-Gordon decay rate n/2(1/p-1/q).