Spectral properties of unbounded symmetric Jacobi matrices are studied. Under mild assumptions on the coefficients absolute continuity of spectral measure is proved. Only operator theoretic proofs are provided. Some open problems of Ifantis are solved.

We consider parabolic equations of porous medium type of the form ut − divA(x, t, u,Du) = μ in ET , in some space time cylinderET . The most prominent example covered by our assumptions is the classical porous medium equation ut −∆u = μ in ET . We establish a sufficient condition for the continuity of u in terms of a natural Riesz potential of the right-hand side measure μ. As an application we...

LetX be a standard probability space and Tt a measure-preserving semiflow on X. We show that there exists a set X0 of full measure in X such that for any x ∈ X0 and t ≥ 0 there are measures μx,t and μ − x,t which for all but a countable number of t give a distribution on the set of points y such that Tt(y) = Tt(x). These measures arise by taking weak∗−limits of suitable conditional expectations...

Classical super-Brownian motion (SBM) is known to take values in the space of absolutely continuous measures only if d=1. For d¿2 its values are almost surely singular with respect to Lebesgue measure. This result has been generalized to more general motion laws and branching laws (yielding di erent critical dimensions) and also to catalytic SBM. In this paper we study the case of a catalytic m...

BACKGROUND Review of the literature reveals a need to develop a questionnaire that measures patient perceptions of factors impacting continuity of care following discharge from hospital. Such a measure has the potential to guide quality improvement initiatives related to continuity of care. OBJECTIVE Our objective was to develop and examine the psychometric properties of a measure that would ...

The paper considers continuity properties of a nite Borel measure on a separable Hilbert space X. Continuity of the mappings x 7 ! (A + x) on a subspace H, uniformly in A 2 B(X), is characterized by the existence of a nonstandard density of having a certain property. This generalizes a well known standard result for measures on R n. The ideas are illustrated with reference to Gaussian measures ...

Working in a continuous time setting, we extend to the general case of dynamic risk measures continuous from above the characterization of time consistency in terms of " cocycle condition " of the minimal penalty function. We prove also the supermartingale property for general time consistent dynamic risk measures. When the time consistent dynamic risk measure (continuous from above) is normali...