In this paper, norm estimates are obtained for the problem of minimal-norm tangential interpolation by vector-valued analytic functions in weighted H spaces, expressed in terms of the Carleson constants of related scalar measures. Applications are given to the notion of p-controllability properties of linear semigroup systems and controllability by functions in certain Sobolev spaces.

This is a survey on reverse Carleson measures for various Hilbert spaces of analytic functions. These spaces include the Hardy, Bergman, certain harmonically weighted Dirichlet, Paley-Wiener, Fock, model (backward shift invariant), and de Branges-Rovnyak spaces. The reverse Carleson measure for backward shift invariant subspaces in the non-Hilbert situation is new.

The present paper is an exposition on heights and their importance in the modern study of algebraic dynamics. We will explain the idea of canonical height and its surprising relation to algebraic dynamics, invariant measures, arithmetic intersection theory, equidistribution and p-adic analytic geometry. AMS Classification 2000: Primary: 14G40; Secondary: 11G50, 28C10, 14C17.

We show an example of a non-archimedean version of the existence part of the Calabi-Yau theorem in complex geometry. Precisely, we study totally degenerate abelian varieties and certain probability measures on their associated analytic spaces in the sense of Berkovich.

A reliable inference of networks from observations of the nodes' dynamics is a major challenge in physics. Interdependence measures such as a the correlation coefficient or more advanced methods based on, e.g., analytic phases of signals are employed. For several of these interdependence measures, multivariate counterparts exist that promise to enable distinguishing direct and indirect connecti...

The complex relationship between structural and functional connectivity, as measured by noninvasive imaging of the human brain, poses many unresolved challenges and open questions. Here, we apply analytic measures of network communication to the structural connectivity of the human brain and explore the capacity of these measures to predict resting-state functional connectivity across three ind...

I t is not hard to see that A and B together are equivalent to the following: The collection of Borel sets on which fi vanishes identically is invariant under rotation. This is the assertion concerning analytic measures that we extend to compact groups. We also shall state several of its consequences, including analogues of A and B. The work was inspired by, and is in part an extension of, seve...

Analytic surgery, as defined in [9] and [6], is a one-parameter metric deformation of a Riemannian manifold M , which stretches M across a separating hypersurface H in a cylindrical fashion; the singular limit is a complete manifold with asymptotically cylindrical ends, M . In this paper, the analysis of [9] and [6] is used to study the behaviour of analytic torsion of unitary representations u...

Theoretically, low correlations between implicit and explicit measures can be due to (a) motivational biases in explicit self reports, (b) lack of introspective access to implicitly assessed representations, (c) factors influencing the retrieval of information from memory, (d) method-related characteristics of the two measures, or (e) complete independence of the underlying constructs. The pres...

This study provides a summary of recently proposed alternatives period measures of "longevity" and assesses whether empirical differences between these measures are consistent with predictions from analytic studies. Particular attention is given to the tempo effect. Three of the five period measures are virtually equal to one another in a simulated population in which mortality follows a Gomper...