Toeplitz operators on Dirichlet-Besov spaces

We study Toeplitz operators on the Besov spaces in the case of the open unit disk. We prove that a symbol satisfying a weak Lipschitz type condition induces a bounded Toeplitz operator. Such symbols do not need to be bounded functions or have continuous extensions to the boundary of the open unit disk. We discuss the problem of the existence of nontrivial compact Toeplitz operators, and also consider Fredholm properties and prove an index formula.

Planning in the face of ‘deep divisions’: a view from Beirut, Lebanon

This article discusses planning in the global South-East while focusing on the specific context of social divides, political turmoil and conflict situations. The article proposes a five-way framework based on political science and planning to theory to analyse such contexts. The article explores the case of Beirut, Lebanon that has undergone several episodes of internal and external conflicts resulting in a society splintered along sectarianism. Three Two case studies of open urban spaces and their public activities are analysed using the five-way framework The discussion indicates how economic liberalism that is prevalent in countries of the South-East, along with place-based identities, interest-based identities, consensus orientated processes and institutionalism might facilitate a cultivation of deep values away from a narrowly constructed identity. The article argues that planners should understand the options for positive action that aim to bridge deep divisions and suggests that the five-way framework provides a reference for contextualising in different ways to suit particular contexts. Therefore, the framework is not necessarily restricted to the South-East but could be applicable to any context which manifests deep divisions.

Adaptive climate change governance for urban resilience

Climate change poses new challenges to cities and new flexible forms of governance are required that are able to take into account the uncertainty and abruptness of changes. The purpose of this paper is to discuss adaptive climate change governance for urban resilience. This paper identifies and reviews three traditions of literature on the idea of transitions and transformations, and assesses to what extent the transitions encompass elements of adaptive governance. This paper uses the open source Urban Transitions Project database to assess how urban experiments take into account principles of adaptive governance. The results show that: the experiments give no explicit information of ecological knowledge; the leadership of cities is primarily from local authorities; and evidence of partnerships and anticipatory or planned adaptation is limited or absent. The analysis shows that neither technological, political nor ecological solutions alone are sufficient to further our understanding of the analytical aspects of transition thinking in urban climate governance. In conclusion, the paper argues that the future research agenda for urban climate governance needs to explore further the links between the three traditions in order to better identify contradictions, complementarities or compatibilities, and what this means in practice for creating and assessing urban experiments.

Urban economic openness and IPO underpricing

We examine the empirical impact of trade openness on the short-run underpricing of initial public offerings (IPOs) using city-level real estate data. This paper represents a first attempt to employ a macroeconomic approach to explain IPO performance. We investigate an openness effect in which urban economic openness (UEO) has a significant impact on the productivity and on the prices of both direct and indirect real estate due to productivity gains of companies in more open areas. This in turn positively affects the firm’s profitability, enhancing the confidence in the local real estate market and the future company performance and decreasing the uncertainty of the IPO valuation. And as a result, we find that issuers have less incentive to underprice the IPO shares. China provides a suitable experimental ground to study the immense underpricing in developing markets, which cannot solely be accounted for by firm specific effects. First, Chinese real estate companies show strong geographic patterns focusing their businesses locally – usually at a city level. Second, we observe a degree of openness which is significantly heterogeneous across Chinese cities. Controlling for company-specific variables, location and state ownership, we find the evidence that companies whose businesses are in economically more open areas experience less IPO underpricing. Our results show high explanatory power and are robust to diverse specifications.