m at h . FA ] 3 0 Ja n 20 06 Pointwise Values and Fundamental Theo - rem in the Algebra of Asymptotic Func - tions

m at h . FA ] 3 1 Ja n 20 06 A HEREDITARILY INDECOMPOSABLE ASYMPTOTIC l 2 BANACH SPACE

A Hereditarily Indecomposable asymptotic ℓ 2 Banach space is constructed. The existence of such a space answers a question of B. Maurey and verifies a conjecture of W.T. Gowers.

ar X iv : m at h / 06 01 74 3 v 1 [ m at h . SP ] 3 0 Ja n 20 06 DETERMINANTS OF ZEROTH ORDER OPERATORS

ar X iv : 0 90 1 . 18 06 v 1 [ m at h . A G ] 1 3 Ja n 20 09 GREENBERG APPROXIMATION AND THE GEOMETRY OF ARC SPACES

We study the differential properties of generalized arc schemes and geometric versions of Kolchin’s Irreducibility Theorem over arbitrary base fields. As an intermediate step, we prove an approximation result for arcs by algebraic curves.

Notes on Matrix Valued Paraproducts

X iv :m at h/ 05 12 40 7v 2 [ m at h. FA ] 1 8 Ja n 20 06 Notes on Matrix Valued Paraproducts Tao MEI 1 Abstract Denote by Mn the algebra of n×n matrices. We consider the dyadic paraproducts πb associated with Mn valued functions b, and show that the L(Mn) norm of b does not dominate ||πb||L2(l2n)→L2(l2n) uniformly over n. We also consider paraproducts associated with noncommutative martingales...

ar X iv : m at h - ph / 0 20 10 06 v 2 1 5 Ja n 20 02 Quasi - classical versus non - classical spectral asymptotics for magnetic Schrödinger operators with decreasing electric potentials

We consider the Schrödinger operator H on L 2 (R 2) or L 2 (R 3) with constant magnetic field, and electric potential V which typically decays at infinity exponentially fast or has a compact support. We investigate the asymptotic behaviour of the discrete spectrum of H near the boundary points of its essential spectrum. If the decay of V is Gaussian or faster, this behaviour is non-classical in...