ar X iv : m at h / 06 06 55 1 v 1 [ m at h . FA ] 2 2 Ju n 20 06 COMPLEX INTERPOLATION OF COMPACT OPERATORS

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 06 67 1 v 1 [ m at h . A C ] 2 7 Ju n 20 06 PRÜFER ⋆ – MULTIPLICATION DOMAINS AND ⋆ – COHERENCE

ar X iv : m at h / 06 06 27 5 v 1 [ m at h . A T ] 1 2 Ju n 20 06 MODULES IN MONOIDAL MODEL CATEGORIES

This paper studies the existence of and compatibility between derived change of ring, balanced product, and function module derived functors on module categories in monoidal model categories.

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 06 67 7 v 1 [ m at h . D S ] 2 7 Ju n 20 06 COMPLEX MAPS WITHOUT INVARIANT DENSITIES

We consider complex polynomials f (z) = z ℓ + c1 for ℓ ∈ 2N and c1 ∈ R, and find some combinatorial types and values of ℓ such that there is no invariant probability measure equivalent to conformal measure on the Julia set. This holds for particular Fibonacci-like and Feigenbaum combinatorial types when ℓ sufficiently large and also for a class of 'long–branched' maps of any critical order.