Vector valued Hardy spaces

The Hardy space $H^{p}$ of vector valued analytic functions in tube domains in $\mathbb{C}^{n}$ and with values in Banach space are defined. Vector valued analytic functions in tube domains in $\mathbb{C}^{n}$ with values in Hilbert space and which have vector valued tempered distributions as boundary value are proved to be in $H^{p}$ corresponding to Hilbert space if the boundary value is in $L^{p}$ with values in Hilbert space. A Poisson integral representation for such vector valued analytic functions is obtained.Comment: 21 page

Note on vector valued Hardy spaces related to analytic functions having distributional boundary values

Analytic functions defined on a tube domain $T^{C}\subset \mathbb{C}^{n}$ and taking values in a Banach space $X$ which are known to have $X$-valued distributional boundary values are shown to be in the Hardy space $H^{p}(T^{C},X)$ if the boundary value is in the vector valued Lebesgue space $L^{p}(\mathbb{R}^{n},X)$, where $1\leq p \leq \infty$ and $C$ is a regular open convex cone. Poisson integral transform representations of elements of $H^{p}(T^{C}, X)$ are also obtained for certain classes of Banach spaces, including reflexive Banach spaces.Comment: 5 page

Holomorphic extension of generalizations of H

In a previous article we have obtained a holomorphic extension theorem (edge of the wedge theorem) concerning holomorphic functions in tubes in ℂn which generalize the Hardy Hp functions for the cases 1<p≤2. In this paper we obtain a similar holomorphic extension theorem for the cases 2<p<∞

Analyzing large-scale conservation interventions with Bayesian hierarchical models: a case study of supplementing threatened Pacific salmon.

Myriad human activities increasingly threaten the existence of many species. A variety of conservation interventions such as habitat restoration, protected areas, and captive breeding have been used to prevent extinctions. Evaluating the effectiveness of these interventions requires appropriate statistical methods, given the quantity and quality of available data. Historically, analysis of variance has been used with some form of predetermined before-after control-impact design to estimate the effects of large-scale experiments or conservation interventions. However, ad hoc retrospective study designs or the presence of random effects at multiple scales may preclude the use of these tools. We evaluated the effects of a large-scale supplementation program on the density of adult Chinook salmon Oncorhynchus tshawytscha from the Snake River basin in the northwestern United States currently listed under the U.S. Endangered Species Act. We analyzed 43 years of data from 22 populations, accounting for random effects across time and space using a form of Bayesian hierarchical time-series model common in analyses of financial markets. We found that varying degrees of supplementation over a period of 25 years increased the density of natural-origin adults, on average, by 0-8% relative to nonsupplementation years. Thirty-nine of the 43 year effects were at least two times larger in magnitude than the mean supplementation effect, suggesting common environmental variables play a more important role in driving interannual variability in adult density. Additional residual variation in density varied considerably across the region, but there was no systematic difference between supplemented and reference populations. Our results demonstrate the power of hierarchical Bayesian models to detect the diffuse effects of management interventions and to quantitatively describe the variability of intervention success. Nevertheless, our study could not address whether ecological factors (e.g., competition) were more important than genetic considerations (e.g., inbreeding depression) in determining the response to supplementation

A pointwise growth estimate for analytic functions in tubes

A class of analytic functions in tube domains TC=ℝn+iC in n-dimensional complex space, where C is an open connected cone in ℝn, which has been defined by V. S. Vladimirov is studied. We show that a previously obtained L2 growth estimate concerning these functions can be replaced by a pointwise growth estimate, and we obtain further new properties of these functions. Our analysis shows that these functions of Vladimirov are exactly the Hardy H2 class of functions corresponding to the tube TC

Growth of H

Let C be an open convex cone in n dimensional real space Rn such that C¯ does not contain any entire straight line. We obtain a growth condition on functions in the Hardy spaces HP(TC), 1≤p≤∞, corresponding to the tube TC=Rn+iC in n dimensional complex space ℂn

Hydrological and associated biogeochemical consequences of rapid global warming during the Paleocene-Eocene Thermal Maximum

The Paleocene-Eocene Thermal Maximum (PETM) hyperthermal, ~ 56 million years ago (Ma), is the most dramatic example of abrupt Cenozoic global warming. During the PETM surface temperatures increased between 5 and 9 °C and the onset likely took < 20 kyr. The PETM provides a case study of the impacts of rapid global warming on the Earth system, including both hydrological and associated biogeochemical feedbacks, and proxy data from the PETM can provide constraints on changes in warm climate hydrology simulated by general circulation models (GCMs). In this paper, we provide a critical review of biological and geochemical signatures interpreted as direct or indirect indicators of hydrological change at the PETM, explore the importance of adopting multi-proxy approaches, and present a preliminary model-data comparison. Hydrological records complement those of temperature and indicate that the climatic response at the PETM was complex, with significant regional and temporal variability. This is further illustrated by the biogeochemical consequences of inferred changes in hydrology and, in fact, changes in precipitation and the biogeochemical consequences are often conflated in geochemical signatures. There is also strong evidence in many regions for changes in the episodic and/or intra-annual distribution of precipitation that has not widely been considered when comparing proxy data to GCM output. Crucially, GCM simulations indicate that the response of the hydrological cycle to the PETM was heterogeneous – some regions are associated with increased precipitation – evaporation (P – E), whilst others are characterised by a decrease. Interestingly, the majority of proxy data come from the regions where GCMs predict an increase in PETM precipitation. We propose that comparison of hydrological proxies to GCM output can be an important test of model skill, but this will be enhanced by further data from regions of model-simulated aridity and simulation of extreme precipitation events

Terrestrial environmental change across the onset of the PETM and the associated impact on biomarker proxies:A cautionary tale

The following supplementary information includes one dataset which contains 3 tables: Biomarker distributions and proxies at Cobham, UK Bulk and compound specific isotope data at Cobham (UK) Model-derived mean annual surface temperature and precipitation estimates as a function of CO2 at Cobham (UK)