1,837 research outputs found

### A quantified Tauberian theorem for sequences

The main result of this paper is a quantified version of Ingham's Tauberian
theorem for bounded vector-valued sequences rather than functions. It gives an
estimate on the rate of decay of such a sequence in terms of the behaviour of a
certain boundary function, with the quality of the estimate depending on the
degree of smoothness this boundary function is assumed to possess. The result
is then used to give a new proof of the quantified Katznelson-Tzafriri theorem
recently obtained in [21]

### Quantified asymptotic behaviour of Banach space operators and applications to iterative projection methods

We present an extension of our earlier work [Ritt operators and convergence
in the method of alternating projections, J. Approx. Theory, 205:133-148, 2016]
by proving a general asymptotic result for orbits of an operator acting on a
reflexive Banach space. This result is obtained under a condition involving the
growth of the resolvent, and we also discuss conditions involving the location
and the geometry of the numerical range of the operator. We then apply the
general results to some classes of iterative projection methods in
approximation theory, such as the Douglas-Rachford splitting method and, under
suitable geometric conditions either on the ambient Banach space or on the
projection operators, the method of alternating projections

### Designing electrical contacts to MoS$_2$ monolayers: A computational study

Studying the reason, why single-layer molybdenum disulfide (MoS$_2$) appears
to fall short of its promising potential in flexible nanoelectronics, we found
that the nature of contacts plays a more important role than the semiconductor
itself. In order to understand the nature of MoS$_2$/metal contacts, we
performed ab initio density functional theory calculations for the geometry,
bonding and electronic structure of the contact region. We found that the most
common contact metal (Au) is rather inefficient for electron injection into
single-layer MoS$_2$ and propose Ti as a representative example of suitable
alternative electrode materials

### Optimal rates of decay for operator semigroups on Hilbert spaces

We investigate rates of decay for $C_0$-semigroups on Hilbert spaces under
assumptions on the resolvent growth of the semigroup generator. Our main
results show that one obtains the best possible estimate on the rate of decay,
that is to say an upper bound which is also known to be a lower bound, under a
comparatively mild assumption on the growth behaviour. This extends several
statements obtained by Batty, Chill and Tomilov (J. Eur. Math. Soc., vol.
18(4), pp. 853-929, 2016). In fact, for a large class of semigroups our
condition is not only sufficient but also necessary for this optimal estimate
to hold. Even without this assumption we obtain a new quantified asymptotic
result which in many cases of interest gives a sharper estimate for the rate of
decay than was previously available, and for semigroups of normal operators we
are able to describe the asymptotic behaviour exactly. We illustrate the
strength of our theoretical results by using them to obtain sharp estimates on
the rate of energy decay for a wave equation subject to viscoelastic damping at
the boundary.Comment: 25 pages. To appear in Advances in Mathematic

### Optimal energy decay for the wave-heat system on a rectangular domain

We study the rate of energy decay for solutions of a coupled wave-heat system
on a rectangular domain. Using techniques from the theory of $C_0$-semigroups,
and in particular a well-known result due to Borichev and Tomilov, we prove
that the energy of classical solutions decays like $t^{-2/3}$ as $t\to\infty$.
This rate is moreover shown to be sharp. Our result implies in particular that
a general estimate in the literature, which predicts at least logarithmic decay
and is known to be best possible in general, is suboptimal in the special case
under consideration here. Our strategy of proof involves direct estimates based
on separation of variables and a refined version of the technique developed in
our earlier paper for a one-dimensional wave-heat system

- â€¦