Abstract We show that an orthogonal root number of a tempered L -parameter $$\varphi $$ φ decomposes as the product two other numbers: principal parameter and value on central involution Langlands’s character for . The formula resolves conjecture Gross Reeder computes numbers Weil–Deligne representations aris...

Let G be a real semisimple Lie group. Harish-Chandra has defined the Schwartz space, V[G), on G. A tempered distribution on G is a continuous linear functional on R G ) . If the real rank of G equals one, Harish-Chandra has published a version of the Plancherel formula for I^(G) [3(k), 5241. We restrict the Fourier transform map to %(G), and we compute the image of the space V(G) [Theorem 31. T...

he modernization project launched by the West two centuries ago, was based on three pillars: State-logic, Capital-logic and Ratio-logic; formulated in part by Montesquieu (France), Smith (Britain) and Kant (Germany). The logic of the State implied centralization of coercive power, tempered by democracy. The logic of Capital implied market forces for economic power, tempered by anti-monopoly cla...

This paper considers the American option pricing problem under the stochastic volatility models. In particular, we introduce the GARCHmodel with two heavy-tailed distributions: classical tempered stable (CTS) and normal tempered stable (NTS) distribution. Then we apply the Markov chain approach to compute the prices of American style options under these two models. Minimal entropy provides a co...

Most of the important models in finance rest on the assumption that randomness is explained through a normal random variable. However there is ample empirical evidence against the normality assumption, since stock returns are heavy-tailed, leptokurtic and skewed. Partly in response to those empirical inconsistencies relative to the properties of the normal distribution, a suitable alternative d...

The Selberg trace formula leads naturally to the study of certain tempered distributions on reductive groups defined over local fields. An important problem is to calculate the Fourier transforms of these distributions. We shall consider this question for the case tha t the local field is R and the group G is semisimple and has real rank one. In this context the notion of the Fourier transform ...

Linking experiments with the atomistic resolution provided by molecular dynamics simulations can shed light on the structure and dynamics of protein-disordered states. The sampling limitations of classical molecular dynamics can be overcome using metadynamics, which is based on the introduction of a history-dependent bias on a small number of suitably chosen collective variables. Even if such b...