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Andreas Hartmann

Publications and source records attributed to Andreas Hartmann.

At least 55 records · Page 3Linked to original sources
arXiv2014

Sampling, interpolation and Riesz bases in small Fock spaces

We give a complete description of Riesz bases of reproducing kernels in small Fock spaces. This characterization is in the spirit of the well known Kadets--Ingham 1/4 theorem for Paley--Wiener spaces. Contrarily to the situation in Paley--Wiener spaces, a link can be established between Riesz bases in the Hilbert case and corresponding complete interpolating sequences in small Fock spaces with associated uniform norm. These results allow to show that if a sequence has a density stricly different from the critical one then either it can be completed or reduced to a complete interpolating sequence. In particular, this allows to give necessary and sufficient conditions for interpolation or sampling in terms of densities.

math.CV↗
arXiv2014

X-ray diffraction from isolated and strongly aligned gas-phase molecules with a free-electron laser

We report experimental results on x-ray diffraction of quantum-state-selected and strongly aligned ensembles of the prototypical asymmetric rotor molecule 2,5-diiodobenzonitrile using the Linac Coherent Light Source. The experiments demonstrate first steps toward a new approach to diffractive imaging of distinct structures of individual, isolated gas-phase molecules. We confirm several key ingredients of single molecule diffraction experiments: the abilities to detect and count individual scattered x-ray photons in single shot diffraction data, to deliver state-selected, e. g., structural-isomer-selected, ensembles of molecules to the x-ray interaction volume, and to strongly align the scattering molecules. Our approach, using ultrashort x-ray pulses, is suitable to study ultrafast dynamics of isolated molecules.

physics.atom-ph↗
arXiv2013

Reverse Carleson measures in Hardy spaces

We give a necessary and sufficient condition for a measure $μ$ in the closed unit disk to be a reverse Carleson measure for Hardy spaces. This extends a previous result of Lefévre, Li, Queffélec and Rodr\'ıguez-Piazza \cite{LLQR}. We also provide a simple example showing that the analogue for the Paley-Wiener space does not hold. This example can be generalised to model spaces associated to one-component inner functions.

math.CV↗
arXiv2012

Reverse Carleson Embeddings for Model Spaces

The classical embedding theorem of Carleson deals with finite positive Borel measures $μ$ on the closed unit disk for which there exists a positive constant $c$ such that $|f|_{L^2(μ)} \leq c |f|_{H^2}$ for all $f \in H^2$, the Hardy space of the unit disk. Lefévre et al. examined measures $μ$ for which there exists a positive constant $c$ such that $\|f\|_{L^2(μ)} \geq c |f|_{H^2}$ for all $f \in H^2$. The first type of inequality above was explored with $H^2$ replaced by one of the model spaces $(ΘH^2)^{\perp}$ by Aleksandrov, Baranov, Cohn, Treil, and Volberg. In this paper we discuss the second type of inequality in $(ΘH^2)^{\perp}$.

math.CV↗
arXiv2012

Bad boundary behavior in star invariant subspaces I

We discuss the boundary behavior of functions in backward shift invariant subspaces $(B H^2)^{\perp}$, where $B$ is a Blaschke product. Extending some results of Ahern and Clark, we are particularly interested in the growth rates of functions at points of the spectrum of $B$ where $B$ does not admit a derivative in the sense of Carathéodory.

math.CV↗
arXiv2010

Boundary values in range spaces of co-analytic truncated Toeplitz operators

Functions in backward shift invariant subspaces have nice analytic continuation properties outside the spectrum of the inner function defining the space. Inside the spectrum of the inner function, Ahern and Clark showed that under some distribution condition on the zeros and the singular measure of the inner function, it is possible to obtain non-tangential boundary values of every function in the backward shift invariant subspace as well as for their derivatives up to a certain order. Here we will investigate, at least when the inner function is a Blaschke product, the non-tangential boundary values of the functions of the backward shift invariant subspace after having applied a co-analytic (truncated) Toeplitz operator. There appears to be a smoothing effect.

math.CV↗
arXiv2010

Extremely weak interpolation in $H^{\infty}$

Given a sequence of points in the unit disk, a well known result due to Carleson states that if given any point of the sequence it is possible to interpolate the value one in that point and zero in all the other points of the sequence, with uniform control of the norm in the Hardy space of bounded analytic functions on the disk, then the sequence is an interpolating sequence (i.e.\ every bounded sequence of values can be interpolated by functions in the Hardy space). It turns out that such a result holds in other spaces. In this short note we would like to show that for a given sequence it is sufficient to find just {\bf one} function interpolating suitably zeros and ones to deduce interpolation in the Hardy space.

math.CV↗
arXiv2010

Coherent interfacial bonding on the FeAs tetrahedron in Fe/Ba(Fe(1-x)Co(x))2As2 bilayers

We demonstrate the growth of epitaxial Fe/Ba(Fe(1-x)Co(x))2As2 (Fe/Ba-122) bilayers on MgO(001) and LSAT(001) single crystal substrates using Pulsed Laser Deposition (PLD). By exploiting the metallic nature of the FeAs tetrahedron in the Ba-122 crystal structure, we achieve a coherent interfacial bond between bcc iron and Co-doped Ba-122. Tc values for both bilayers were close to that of the PLD target. Direct observation of interfacial bonding between Fe and the Ba-122 FeAs sublattice by atomic resolution transmission electron microscopy implies that this bilayer architecture may work for other iron pnictide systems and pave the way for the fabrication of superconducting/ferromagnetic heterostructures.

cond-mat.supr-con↗
arXiv2009

Uniform minimality, unconditionality and interpolation in backward shift invariant spaces

We discuss relations between uniform minimality, unconditionality and interpolation for families of reproducing kernels in backward shift invariant subspaces. This class of spaces contains as prominent examples the Paley-Wiener spaces for which it is known that uniform minimality does in general neither imply interpolation nor unconditionality. Hence, contrarily to the situation of standard Hardy spaces (and other scales of spaces), changing the size of the space seems %in this context necessary to deduce unconditionality or interpolation from uniform minimality. Such a change can take two directions: lowering the power of integration, or "increasing" the defining inner function (e.g. increasing the type in the case of Paley-Wiener space). Khinchin's inequalities play a substantial rôle in the proofs of our main results.

math.CV↗
arXiv2008

Analytic continuation and embeddings in weighted backward shift invariant subspaces

By a famous result, functions in backward shift invariant subspaces in Hardy spaces are characterized by the fact that they admit a pseudocontinuation a.e. on $\T$. More can be said if the spectrum of the associated inner function has holes on $\T$. Then the functions of the invariant subspaces even extend analytically through these holes. We will discuss the situation in weighted backward shift invariant subspaces. The results on analytic continuation will be applied to consider some embeddings of weighted invariant subspaces into their unweighted companions. Such weighted versions of invariant subspaces appear naturally in the context of Toeplitz operators. A connection between the spectrum of the inner function and the approximate point spectrum of the backward shift in the weighted situation is established in the spirit of results by Aleman, Richter and Ross.

math.CV↗
arXiv2008

Thermal Conductivity from Core and Well log Data

The relationships between thermal conductivity and other petrophysical properties have been analysed for a borehole drilled in a Tertiary Flysch sequence. We establish equations that permit us to predict rock thermal conductivity from logging data. A regression analysis of thermal conductivity, bulk density, and sonic velocity yields thermal conductivity with an average accuracy of better than 0.2 W/(m K). As a second step, logging data is used to compute a lithological depth profile, which in turn is used to calculate a thermal conductivity profile. From a comparison of the conductivity-depth profile and the laboratory data it can be concluded that thermal conductivity can be computed with an accuracy of less than 0.3 W/(m K)from conventional wireline data. The comparison of two different models shows that this approach can be practical even if old and incomplete logging data is used. The results can be used to infer thermal conductivity for boreholes without appropriate core data that are drilled in a similar geological setting.

physics.geo-ph↗
arXiv2008

Uncertainties and shortcomings of ground surface temperature histories derived from inversion of temperature logs

Analysing borehole temperature data in terms of ground surface history can add useful information to reconstructions of past climates. Therefore, a rigorous assessment of uncertainties and error sources is a necessary prerequisite for the meaningful interpretation of such ground surface temperature histories. This study analyses the most prominent sources of uncertainty. The diffusive nature of the process makes the inversion relatively robust against incomplete knowledge of the thermal diffusivity. Similarly the influence of heat production is small. It turns out that for investigations of the last 1000 to 100000 years the maximum depth of the temperature log is crucial. More than 3000 m are required for an optimal inversion. Reconstructions of the last one or two millennia require only modestly deep logs (>300 m) but suffer severely from noisy data.

physics.geo-ph↗
arXiv2008

Inversion of marine heat flow measurements by expansion of the temperature decay function

Marine heat flow data, obtained with a Lister-type probe, consists of two temperature decay curves, frictional and heat pulse decay. Both follow the same physical model of a cooling cylinder. The mathematical model describing the decays is non-linear as to the thermal sediment parameters thus a direct inversion is not possible. To overcome this difficulty, the model equations are expanded using a first-orderTaylor series. The linearised model equations are used in an iterative scheme to invert the temperature decay for undisturbed temperature and thermal conductivity of the sediment. The inversion scheme is tested first for its theoretical limitations using synthetic data. Inversion of heat flow measurements obtained during a cruise of R/V SONNE in 1996 and needle probe measurements in material of known thermal conductivity show that the algorithm is robust and gives reliable results. The programme can be obtained from the authors.

physics.geo-ph↗
arXiv2008

Petrophysical analysis of regional-scale thermal properties for improved simulations of geothermal installations and basin-scale heat and fluid flow

Development of geothermal energy and basin-scale simulations of fluid and heat flow both suffer from uncertain physical rock properties at depth. Therefore, building better prognostic models are required. We analysed hydraulic and thermal properties of the major rock types in the Molasse Basin in Southern Germany. On about 400 samples thermal conductivity, density, porosity, and sonic velocity were measured. Here, we propose a three-step procedure with increasing complexity for analysis of the data set: First, univariate descriptive statistics provides a general understanding of the data structure, possibly still with large uncertainty. Examples show that the remaining uncertainty can be as high as 0.8 W/(m K) or as low as 0.1 W/(m K). This depends on the possibility to subdivide the geologic units into data sets that are also petrophysically similar. Then, based on all measurements, cross-plot and quick-look methods are used to gain more insight into petrophysical relationships and to refine the analysis. Because these measures usually imply an exactly determined system they do not provide strict error bounds. The final, most complex step comprises a full inversion of select subsets of the data comprising both laboratory and borehole measurements. The example presented shows the possibility to refine the used mixing laws for Petrophysical properties and the estimation of mineral properties. These can be estimated to an accuracy of 0.3 W/(m K). The predictive errors for the measurements are 0.07 W/(m K), 70 m/s, and 8 kg/m^3 for thermal conductivity, sonic velocity, and bulk density, respectively.

physics.geo-ph↗
arXiv2007

Pointwise multipliers in Hardy-Orlicz spaces, and interpolation

We study multipliers of Hardy-Orlicz spaces $\mH_Φ$ which are strictly contained between $\bigcup_{p>0}H^p$ and so-called ``big'' Hardy-Orlicz spaces. Big Hardy-Orlicz spaces, carrying an algebraic structure, are equal to their multiplier algebra, whereas in classical Hardy spaces $H^p$, the multipliers reduce to $H^{\infty}$. For Hardy-Orlicz spaces $\mH_Φ$ between these two extremal situations and subject to some conditions, we exhibit multipliers that are in Hardy-Orlicz spaces the defining functions of which are related to $Φ$. Even if the results do not entirely characterize the multiplier algebra, some examples show that we are not very far from precise conditions. In certain situations we see how the multiplier algebra grows in a sense from $\Hi$ to big Hardy-Orlicz spaces when we go from classical $H^p$ spaces to big Hardy-Orlicz spaces. However, the multiplier algebras are not always ordered as their underlying Hardy-Orlicz spaces. Such an ordering holds in certain situations, but examples show that there are large Hardy-Orlicz spaces for which the multipliers reduce to $\Hi$ so that the multipliers do in general not conserve the ordering of the underlying Hardy-Orlicz spaces. We apply some of the multiplier results to construct Hardy-Orlicz spaces close to $\bigcup_{p>0}H^p$ and for which the free interpolating sequences are no longer characterized by the Carleson condition which is well known to characterize free interpolating sequences in $H^p$, $p>0$.

math.CV↗