Approximations of strongly continuous families of unbounded self-adjoint operators

The problem of approximating the discrete spectra of families of self-adjoint operators that are merely strongly continuous is addressed. It is well-known that the spectrum need not vary continuously (as a set) under strong perturbations. However, it is shown that under an additional compactness assumption the spectrum does vary continuously, and a family of symmetric finite-dimensional approximations is constructed. An important feature of these approximations is that they are valid for the entire family uniformly. An application of this result to the study of plasma instabilities is illustrated.Comment: 22 pages, final version to appear in Commun. Math. Phy

Exploring the landscape of reflection

open4noopenFrison, Daniela; Fedeli, Monica; Tino, Concetta; Minnoni, ErikaFrison, Daniela; Fedeli, Monica; Tino, Concetta; Minnoni, Erik

Uniqueness and stability for the Vlasov-Poisson system with spatial density in Orlicz spaces

In this paper, we establish uniqueness of the solution of the Vlasov-Poisson system with spatial density belonging to a certain class of Orlicz spaces. This extends the uniqueness result of Loeper (which holds for uniformly bounded density) and the uniqueness result of the second author. Uniqueness is a direct consequence of our main result, which provides a quantitative stability estimate for the Wasserstein distance between two weak solutions with spatial density in such Orlicz spaces, in the spirit of Dobrushin's proof of stability for mean-field PDEs. Our proofs are built on the second-order structure of the underlying characteristic system associated to the equation

Holding periods and investment performance: analysing UK office returns 1983-2003

Drawing on a unique database of office properties constructed for Gerald Eve by IPD, this paper examines the holding periods of individual office properties sold between 1983 and 2003. It quantifies the holding periods of sold properties and examines the relationship between the holding period and investment performance. Across the range of holding periods, excess returns (performance relative to the market) are evenly distributed. There are as many winners as there are losers. The distribution of excess returns over different holding periods is widely spread with the risk of under-performance greater over short holding periods. Over the longer term, excess performance is confined to a narrow range and individual returns are more likely to perform in line with the market as a whole

Holding On To History

When I searched for the story of Georges Lieber, the very man whose drive to resist inspired the concept for this essay, I could not find it. The only trace of him was his record on the Yad Vashem database which merely states that he was a student and that he was transported from Lyon, France to Auschwitz in 1944. His story, along with much of Holocaust history, remains unknown or misunderstood for many people, both from my generation and those before us. As a long-term student of history and an aspiring educator, I have chosen to resist the sliding grip that people have on history and hoist it up before the lives and lessons in it are lost

Liquidity and Asset Pricing: Evidence on the Role of Investor Holding Period

We use data on actual holding periods for all investors in a stock market over a 10-year period to investigate the links between holding periods, liquidity, and asset returns. Microstructure measures of liquidity are shown to be important determinants of the holding period decision of individual investors. Average holding periods differ across different investor types. Turnover is an imperfect proxy for holding period. While both turnover and spread are related to stock returns, holding period is not.Market microstructure; Holding period; duration