ar X iv : 0 90 3 . 21 97 v 2 [ m at h . A C ] 2 5 Ju n 20 09 Hardy type derivations on generalized series fields

ar X iv : 0 90 7 . 28 62 v 1 [ m at h . FA ] 1 6 Ju l 2 00 9 On the stability of J ∗ − derivations

In this paper, we establish the stability and superstability of J∗−derivations in J∗−algebras for the generalized Jensen–type functional equation rf( x+ y r ) + rf( x− y r ) = 2f(x). Finally, we investigate the stability of J∗−derivations by using the fixed point alternative.

ar X iv : 0 80 5 . 12 35 v 2 [ m at h . G R ] 3 0 Ju n 20 09 SCHUR – WEYL DUALITY OVER FINITE FIELDS

We prove a version of Schur–Weyl duality over finite fields. We prove that for any field k, if k has at least r + 1 elements, then Schur– Weyl duality holds for the rth tensor power of a finite dimensional vector space V . Moreover, if the dimension of V is at least r + 1, the natural map kSr → EndGL(V )(V ) is an isomorphism. This isomorphism may fail if dimk V is not strictly larger than r.

ar X iv : 0 90 6 . 48 35 v 1 [ m at h . O C ] 2 6 Ju n 20 09 The Complex Gradient Operator and the CR - Calculus

ar X iv : 0 90 1 . 44 03 v 3 [ m at h . C T ] 2 5 Ju n 20 09 A * - autonomous Category of Banach Spaces – Corrected

We describe a C-linear additive *-autonomous category of Banach spaces. Please note that a correction has been appended to the original version 1 which is maintained here for reference. Also, a proposed example of a *-autonomous category of topological C-linear spaces has been added to version 2.

ar X iv : 0 90 6 . 33 84 v 1 [ m at h . A P ] 1 8 Ju n 20 09 ENERGY DISPERSED LARGE DATA WAVE MAPS IN 2 + 1 DIMENSIONS

In this article we consider large data Wave-Maps from R into a compact Riemannian manifold (M, g), and we prove that regularity and dispersive bounds persist as long as a certain type of bulk (non-dispersive) concentration is absent. This is a companion to our concurrent article [21], which together with the present work establishes a full regularity theory for large data Wave-Maps.