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

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

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 / 05 06 18 3 v 1 [ m at h . FA ] 1 0 Ju n 20 05 THE TRIANGLE OF OPERATORS , TOPOLOGIES , BORNOLOGIES

This paper discusses two common techniques in functional analysis: the topological method and the bornological method. In terms of Pietsch’s operator ideals, we establish the equivalence of the notions of operators, topologies and bornologies. The approaches in the study of locally convex spaces of Grothendieck (via Banach space operators), Randtke (via continuous seminorms) and Hogbe-Nlend (vi...

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 - ph / 9 90 70 23 v 1 2 8 Ju l 1 99 9 EIGENFUNCTIONS , TRANSFER MATRICES , AND ABSOLUTELY CONTINUOUS SPECTRUM OF ONE - DIMENSIONAL SCHRÖDINGER OPERATORS

In this paper, we will primarily discuss one-dimensional discrete Schrödinger operators (hu)(n) = u(n + 1) + u(n − 1) + V (n)u(n) (1.1D) on ℓ 2 (Z) (and the half-line problem, h + , on ℓ 2 ({n ∈ Z | n > 0}) ≡ ℓ 2 (Z +)) with u(0) = 0 boundary conditions. We will also discuss the continuum analog (Hu)(x) = −u ′′ (x) + V (x)u(x) (1.1C) on L 2 (R) (and its half-line problem, H + , on L 2 (0, ∞) wi...

0 . 08 70 v 2 [ m at h . FA ] 5 N ov 2 01 0 IRREDUCIBLE WAVELET REPRESENTATIONS AND ERGODIC AUTOMORPHISMS ON SOLENOIDS

We focus on the irreducibility of wavelet representations. We present some connections between the following notions: covariant wavelet representations, ergodic shifts on solenoids, fixed points of transfer (Ruelle) operators and solutions of refinement equations. We investigate the irreducibility of the wavelet representations, in particular the representation associated to the Cantor set, int...