Composition operators on vector-valued BMOA and related function spaces

A composition operator is a linear operator between spaces of analytic or harmonic functions on the unit disk, which precomposes a function with a fixed self-map of the disk. A fundamental problem is to relate properties of a composition operator to the function-theoretic properties of the self-map. During the recent decades these operators have been very actively studied in connection with various function spaces. The study of composition operators lies in the intersection of two central fields of mathematical analysis; function theory and operator theory. This thesis consists of four research articles and an overview. In the first three articles the weak compactness of composition operators is studied on certain vector-valued function spaces. A vector-valued function takes its values in some complex Banach space. In the first and third article sufficient conditions are given for a composition operator to be weakly compact on different versions of vector-valued BMOA spaces. In the second article characterizations are given for the weak compactness of a composition operator on harmonic Hardy spaces and spaces of Cauchy transforms, provided the functions take values in a reflexive Banach space. Composition operators are also considered on certain weak versions of the above function spaces. In addition, the relationship of different vector-valued function spaces is analyzed. In the fourth article weighted composition operators are studied on the scalar-valued BMOA space and its subspace VMOA. A weighted composition operator is obtained by first applying a composition operator and then a pointwise multiplier. A complete characterization is given for the boundedness and compactness of a weighted composition operator on BMOA and VMOA. Moreover, the essential norm of a weighted composition operator on VMOA is estimated. These results generalize many previously known results about composition operators and pointwise multipliers on these spaces.Väitöskirjassa tutkitaan kompositio-operaattoreita kompleksitason yksikkökiekon analyyttisten ja harmonisten funktioiden avaruuksissa. Kompositio-operaattori on lineaarinen kuvaus, joka yhdistää funktioon sisältä päin symbolin eli jonkin analyyttisen kuvauksen yksikkökiekolta itselleen. Tutkimuksen tavoitteena on kuvata kompositio-operaattorin ominaisuuksia symbolin funktioteoreettisten ominaisuuksien avulla. Viimeisten vuosikymmenien aikana kompositio-operaattoreita on tutkittu aktiivisesti eri funktioavaruuksissa. Tutkimus sijoittuu kahden keskeisen matemaattisen analyysin osa-alueen, funktioteorian ja operaattoriteorian leikkaukseen. Väitöskirja koostuu neljästä artikkelista ja yhteenveto-osasta. Ensimmäisessä ja kolmannessa artikkelissa annetaan riittäviä ehtoja kompositio-operaattorin heikolle kompaktisuudelle vektoriarvoisissa BMOA-avaruuksissa ja sen eri versioissa. Toisessa artikkelissa karakterisoidaan operaattorin heikko kompaktisuus vektoriarvoisissa harmonisissa Hardy-avaruuksissa ja Cauchy-muunnosten avaruuksissa. Kompositio-operaattoreita tutkitaan myös näiden avaruuksien heikoissa versioissa. Lisäksi eri avaruuksien välisiä eroja valaistaan esimerkein. Viimeisessä artikkelissa tutkitaan painotettuja kompositio-operaattoreita skalaariarvoisessa BMOA-avaruudessa ja sen aliavaruudessa VMOA. Painotettu kompositio-operaattori saadaan soveltamalla ensin kompositio-operaattoria ja sitten pisteittäistä multiplikaattoria. Työssä karakterisoidaan painotetun kompositio-operaattorin kompaktisuus BMOA-avaruudessa ja annetaan arvio operaattorin olennaiselle normille VMOA-avaruudessa. Nämä tulokset yleistävät monia aikaisemmin tunnettuja kompositio-operaattoreita ja multiplikaattoreita koskevia tuloksia

Weak compactness and essential norms of integration operators

Let $g$ be an analytic function on the unit disc and consider the integration operator of the form $T_g f(z) = \int_0^z fg'\,d\zeta$. We show that on the spaces $H^1$ and $BMOA$ the operator $T_g$ is weakly compact if and only if it is compact. In the case of $BMOA$ this answers a question of Siskakis and Zhao. More generally, we estimate the essential and weak essential norms of $T_g$ on $H^p$ and $BMOA$

FORUM : Indirect leakage leads to a failure of avoided loss biodiversity offsetting

Biodiversity offsetting has quickly gained political support all around the world. Avoided loss (averted risk) offsetting means compensation for ecological damage via averted loss of anticipated impacts through the removal of threatening processes in compensation areas. Leakage means the phenomenon of environmentally damaging activity relocating elsewhere after being stopped locally by avoided loss offsetting. Indirect leakage means that locally avoided losses displace to other administrative areas or spread around diffusely via market effects. Synthesis and applications. Indirect leakage can lead to high net biodiversity loss. It is difficult to measure or prevent, raising doubts about the value of avoided loss offsetting. Market demand for commodities is on the rise, following increasing human population size and per capita consumption, implying that indirect leakage will be a rule rather than an exception. Leakage should be accounted for when determining offset multipliers (ratios) even if multipliers become extremely high.Peer reviewe

A method for calculating minimum biodiversity offset multipliers accounting for time discounting, additionality and permanence

Peer reviewe

The cost competitiveness of conifer stumps in the procurement of forest chips for fuel in Southern and Northern Finland

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New performance guarantees for the greedy maximization of submodular set functions

We present new tight performance guarantees for the greedy maximization of monotone submodular set functions. Our main result first provides a performance guarantee in terms of the overlap of the optimal and greedy solutions. As a consequence we improve performance guarantees of Nemhauser et al. (Math Program 14: 265-294, 1978) and Conforti and Cornuejols (Discr Appl Math 7: 251-274, 1984) for maximization over subsets, which are at least half the size of the problem domain. As a further application, we obtain a new tight approximation guarantee in terms of the cardinality of the problem domain.Peer reviewe

Prototype of hybrid technology chipper-D4.6

INFRES - Innovative and effective technology and logistics for forest residual biomass supply in the EU (311881) is a collaborative project co-funded under the European Commission's FP7 Work Programme 2012 (FP7-KBBE-2012.1.2-01)201

Identification of policies for a sustainable legal trade in rhinoceros horn based on population projection and socioeconomic models

Between 1990 and 2007, 15 southern white (Ceratotherium simum simum) and black (Diceros bicornis) rhinoceroses on average were killed illegally every year in South Africa. Since 2007 illegal killing of southern white rhinoceros for their horn has escalated to >950 individuals/year in 2013. We conducted an ecological-economic analysis to determine whether a legal trade in southern white rhinoceros horn could facilitate rhinoceros protection. Generalized linear models were used to examine the socioeconomic drivers of poaching, based on data collected from 1990 to 2013, and to project the total number of rhinoceroses likely to be illegally killed from 2014 to 2023. Rhinoceros population dynamics were then modeled under 8 different policy scenarios that could be implemented to control poaching. We also estimated the economic costs and benefits of each scenario under enhanced enforcement only and a legal trade in rhinoceros horn and used a decision support framework to rank the scenarios with the objective of maintaining the rhinoceros population above its current size while generating profit for local stakeholders. The southern white rhinoceros population was predicted to go extinct in the wild <20 years under present management. The optimal scenario to maintain the rhinoceros population above its current size was to provide a medium increase in antipoaching effort and to increase the monetary fine on conviction. Without legalizing the trade, implementing such a scenario would require covering costs equal to approximately $147,000,000/year. With a legal trade in rhinoceros horn, the conservation enterprise could potentially make a profit of$717,000,000/year. We believe the 35-year-old ban on rhinoceros horn products should not be lifted unless the money generated from trade is reinvested in improved protection of the rhinoceros population. Because current protection efforts seem to be failing, it is time to evaluate, discuss, and test alternatives to the present policy.Peer reviewe