MathSciDoc: An Archive for Mathematician ∫

Using rearrangements of matrix-valued sequences, we prove that with certain boundary conditions the solution of the one-dimensional Schrödinger equation increases or decreases under monotone rearrangements of its potential.

No abstract uploaded!

We compute the$L$^{$p$}-cohomology spaces of some negatively curved manifolds. We deal with two cases: manifolds with finite volume and sufficiently pinched negative curvature, and conformally compact manifolds.

An asymptotic formula is given for the number of integers$n$≤$x$for which φ($n$) is not divisible by a given odd prime.

In this paper, we generalize a theorem of Kallman [2, Theorem 1.1] and we resolve the unsettled case there.

No abstract uploaded!

We prove that the absolutely continuous subspace of the completely non-selfadjoint part of a first-order dissipative Dirac-like system is trivial when the imaginary part of the potential is non-integrable.

The problem of$subextension$of plurisubharmonic functions is considered. Recently it was shown by Cegrell–Zeriahi, that subextension is always possible for negative plurisubharmonic functions in the energy class ℱ. In this paper we construct, for every hyperconvex domain Ω, a negative plurisubharmonic function in the class ℰ which cannot be subextended. Given any pseudoconvex domain we construct a pluriharmonic function that cannot be subextended.

Auslander–Reiten sequences are the central item of Auslander–Reiten theory, which is one of the most important techniques for the investigation of the structure of abelian categories.

No abstract uploaded!