An integral representation for Besov and Lipschitz spaces

It is well known that functions in the analytic Besov space $B_1$ on the unit disk \D admits an integral representation f(z)=\ind\frac{z-w}{1-z\bar w}\,d\mu(w), where $\mu$ is a complex Borel measure with |\mu|(\D)<\infty. We generalize this result to all Besov spaces $B_p$ with $0<p\le1$ and all Lipschitz spaces $\Lambda_t$ with $t>1$. We also obtain a version for Bergman and Fock spaces

Exploring personality-targeted UI design in online social participation systems

We present a theoretical foundation and empirical findings demonstrating the effectiveness of personality-targeted design. Much like a medical treatment applied to a person based on his specific genetic profile, we argue that theory-driven, personality-targeted UI design can be more effective than design applied to the entire population. The empirical exploration focused on two settings, two populations and two personality traits: Study 1 shows that users' extroversion level moderates the relationship between the UI cue of audience size and users' contribution. Study 2 demonstrates that the effectiveness of social anchors in encouraging online contributions depends on users' level of emotional stability. Taken together, the findings demonstrate the potential and robustness of the interactionist approach to UI design. The findings contribute to the HCI community, and in particular to designers of social systems, by providing guidelines to targeted design that can increase online participation. Copyright © 2013 ACM

Berezin transform on the quantum unit ball

We introduce and study, in the framework of a theory of quantum Cartan domains, a q-analogue of the Berezin transform on the unit ball. We construct q-analogues of weighted Bergman spaces, Toeplitz operators and covariant symbol calculus. In studying the analytical properties of the Berezin transform we introduce also the q-analogue of the SU(n,1)-invariant Laplace operator (the Laplace-Beltrami operator) and present related results on harmonic analysis on the quantum ball. These are applied to obtain an analogue of one result by A.Unterberger and H.Upmeier. An explicit asymptotic formula expressing the q-Berezin transform via the q-Laplace-Beltrami operator is also derived. At the end of the paper, we give an application of our results to basic hypergeometric q-orthogonal polynomials.Comment: 38 pages, accepted by Journal of Mathematical Physic

Balanced metrics on Cartan and Cartan-Hartogs domains

This paper consists of two results dealing with balanced metrics (in S. Donaldson terminology) on nonconpact complex manifolds. In the first one we describe all balanced metrics on Cartan domains. In the second one we show that the only Cartan-Hartogs domain which admits a balanced metric is the complex hyperbolic space. By combining these results with those obtained in [13] (Kaehler-Einstein submanifolds of the infinite dimensional projective space, to appear in Mathematische Annalen) we also provide the first example of complete, Kaehler-Einstein and projectively induced metric g such that $\alpha g$ is not balanced for all $\alpha >0$.Comment: 11 page

Weyl invariant polynomial and deformation quantization on Kahler manifolds

Given a polynomial P of partial derivatives of the Kahler metric, expressed as a linear combination of directed multigraphs, we prove a simple criterion in terms of the coefficients for $P$ to be an invariant polynomial, i.e. invariant under the transformation of coordinates. As applications, we prove an explicit composition formula for covariant differential operators under a canonical basis, also known as invariant differential operators in the case of bounded symmetric domains. We also prove a general explicit formula of star products on Kahler manifolds.Comment: 17 page

Wigner transform and pseudodifferential operators on symmetric spaces of non-compact type

We obtain a general expression for a Wigner transform (Wigner function) on symmetric spaces of non-compact type and study the Weyl calculus of pseudodifferential operators on them

On fixed points of self maps of the free ball

In this paper, we study the structure of the fixed point sets of noncommutative self maps of the free ball. We show that for such a map that fixes the origin the fixed point set on every level is the intersection of the ball with a linear subspace. We provide an application for the completely isometric isomorphism problem of multiplier algebras of noncommutative complete Pick spaces