ar X iv : 1 71 2 . 06 96 9 v 1 [ m at h . N T ] 1 9 D ec 2 01 7 THETA OPERATORS ON UNITARY SHIMURA VARIETIES

ar X iv : 1 71 2 . 05 94 9 v 1 [ m at h . M G ] 1 6 D ec 2 01 7 ESTIMATES FOR MOMENTS OF GENERAL MEASURES ON CONVEX BODIES

ar X iv : m at h / 06 06 33 9 v 1 [ m at h . SP ] 1 4 Ju n 20 06 Eigenfunction expansions associated with 1 d periodic differential operators of order 2 n

We prove an explicit formula for the spectral expansions in L(R) generated by selfadjoint differential operators (−1) d dx2n + n−1

ar X iv : m at h / 06 12 24 2 v 1 [ m at h . A P ] 9 D ec 2 00 6 Optimal Uniform Elliptic Estimates for the Ginzburg - Landau System

We reconsider the elliptic estimates for magnetic operators in two and three dimensions used in connection with Ginzburg-Landau theory. Furthermore we discuss the so-called blow-up technique in order to obtain optimal estimates in the limiting cases.

ar X iv : s ol v - in t / 9 71 00 19 v 1 2 3 O ct 1 99 7 D - MODULES AND DARBOUX TRANSFORMATIONS

A method of G. Wilson for generating commutative algebras of ordinary differential operators is extended to higher dimensions. Our construction, based on the theory of D-modules, leads to a new class of examples of commutative rings of partial differential operators with rational spectral varieties. As an application, we briefly discuss their link to the bispectral problem and to the theory of ...

ar X iv : m at h / 06 11 81 9 v 2 [ m at h . D G ] 1 2 Ja n 20 07 EQUIVARIANT AND FRACTIONAL INDEX OF PROJECTIVE ELLIPTIC OPERATORS

In this note the fractional analytic index, for a projective elliptic operator associated to an Azumaya bundle, of [4] is related to the equivariant index of [1, 5] for an associated transversally elliptic operator.