ar X iv : m at h / 07 01 45 3 v 2 [ m at h . FA ] 1 8 Ja n 20 07 COVARIANT REPRESENTATIONS FOR MATRIX - VALUED TRANSFER OPERATORS

ar X iv : m at h / 07 01 45 3 v 3 [ m at h . FA ] 2 8 Ju n 20 07 COVARIANT REPRESENTATIONS FOR MATRIX - VALUED TRANSFER OPERATORS

Motivated by the multivariate wavelet theory, and by the spectral theory of transfer operators, we construct an abstract affine structure and a multiresolution associated to a matrix-valued weight. We describe the one-to-one correspondence between the commutant of this structure and the fixed points of the transfer operator. We show how the covariant representation can be realized on Rn if the ...

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 : m at h / 05 01 45 4 v 2 [ m at h . A G ] 1 2 Ja n 20 06 HIGHER NOETHER - LEFSCHETZ LOCI OF ELLIPTIC SURFACES

We calculate the dimension of the locus of Jacobian elliptic surfaces over P with given Picard number, in the corresponding moduli space.

ar X iv : m at h / 04 01 12 6 v 1 [ m at h . N T ] 1 3 Ja n 20 04 THREE LECTURES ON THE RIEMANN ZETA - FUNCTION

ar X iv : m at h / 06 01 47 2 v 1 [ m at h . Q A ] 1 9 Ja n 20 06 REPRESENTATIONS OF QUANTUM GROUPS DEFINED OVER COMMUTATIVE RINGS II

In this article we study the structure of highest weight modules for quantum groups defined over a commutative ring with particular emphasis on the structure theory for invariant bilinear forms on these modules.