Factorization of weakly continuous holomorphic mappings

We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly continuous on weakly bounded sets if and only if it is weakly {\it uniformly\/} continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Herv\'es and Valdivia for polynomials between Banach spaces, and it also holds if the weak topology is replaced by a coarser one. However, we show that it need not be true for a stronger topology, thus answering a question raised by Aron. As an application of the first result, we prove that a holomorphic mapping $f$ between complex Banach spaces is weakly uniformly continuous on bounded subsets if and only if it admits a factorization of the form $f=g\circ S$, where $S$ is a compact operator and $g$ a holomorphic mapping

On LpL^p--LqL^q trace inequalities

We give necessary and sufficient conditions in order that inequalities of the type $$\| T_K f\|_{L^q(d\mu)}\leq C \|f\|_{L^p(d\sigma)}, \qquad f \in L^p(d\sigma),$$ hold for a class of integral operators $T_K f(x) = \int_{R^n} K(x, y) f(y) d \sigma(y)$ with nonnegative kernels, and measures $d \mu$ and $d\sigma$ on $\R^n$, in the case where $p>q>0$ and $p>1$. An important model is provided by the dyadic integral operator with kernel $K_{\mathcal D}(x, y) \sum_{Q\in{\mathcal D}} K(Q) \chi_Q(x) \chi_Q(y)$, where $\mathcal D=\{Q\}$ is the family of all dyadic cubes in $\R^n$, and $K(Q)$ are arbitrary nonnegative constants associated with $Q \in{\mathcal D}$. The corresponding continuous versions are deduced from their dyadic counterparts. In particular, we show that, for the convolution operator $T_k f = k\star f$ with positive radially decreasing kernel $k(|x-y|)$, the trace inequality $$\| T_k f\|_{L^q(d\mu)}\leq C \|f\|_{L^p(d x)}, \qquad f \in L^p(dx),$$ holds if and only if ${\mathcal W}_{k}[\mu] \in L^s (d\mu)$, where $s = {\frac{q(p-1)}{p-q}}$. Here ${\mathcal W}_{k}[\mu]$ is a nonlinear Wolff potential defined by ${\mathcal W}_{k}[\mu](x)=\int_0^{+\infty} k(r) \bar{k}(r)^{\frac 1 {p-1}} \mu (B(x,r))^{\frac 1{p-1}} r^{n-1} dr,$ and $\bar{k}(r)=\frac1{r^n}\int_0^r k(t) t^{n-1} dt$. Analogous inequalities for $1\le q < p$ were characterized earlier by the authors using a different method which is not applicable when $q<1$

On quotients of holomorphic functions in the disc with boundary regularity conditions

In this paper we give characterizations of those holomorphic functions in the unit disc in the complex plane that can be written as a quotient of functions in A(D), A°°(D) or Al(D) with a nonvanishing denominator in D. As a consequence we prove that if f E Al (D) does not vanish in D, then there exists g E Al (D) which has the same zero set as f in D and such that fg E A(D)

P.A. in the era of competitive sourcing: Quality, qualitatively

Among President George W. Bush\u27s management initiatives, competitive sourcing was the most complex, most challenging, and most politicized, admitted Angela Styles, chief of procurement policy at the Office of Management and Budget (OMB), in 2002. Styles had left OMB when I started my research but behind her the battle raged on how to subject thousands of federal commercial jobs for public private competition under the rules of Circular A-76 and according to performance criteria set by the OMB Scorecard. In competitive sourcing, if contractors can perform the job more efficiently than the govemment team, the work is outsourced and the affected employees are terminated or reassigned within the organization. Early in the Bush Administration the policy preference was for a limited duration of awards if the feds should win and recompetition to be held every five years

Contract management: A P.A. education for boundary managers.

Graduates of public administration programs might reasonably be expected to accurately spell out, even in their sleep, POSDCoRB. After all, it was Luther Gulick\u27s rock-hewn formulation of the skills involved in public administration, circa 1937. Almost seven decades later, in their book Governing by Network, Stephen Goldsmith and William Eggers called for acultural transformation in the way we build capacity in the public sector, and, as I see it, crafting a new POSDCoRB for our time

Functional differentiation within the monkey cortex as revealed by near-infrared spectroscopy

The role of prefrontal cortex in working memory (WM) is well established. However, questions remain regarding the topography and &#x201c;domain-specific differentiation&#x201d; of different types of information processing in the cortex. While it has been theorized that dorsolateral (DPFC) and ventrolateral (VPFC) prefrontal cortex preferentially process spatial and object WM, respectively, both electrophysiological evidence in the monkey and neuroimaging in the human have largely failed to demonstrate such regional differentiation. In this study we use near-infrared spectroscopy (NIRS) to detect functional changes, across relatively large cortical cell populations, simultaneously from prefrontal and posterior parietal cortices. Imaging data were recorded from a Rhesus macaque performing two types of WM tasks: a spatial task in which the animal had to retain the spatial position of a visual stimulus, and a non-spatial task where he had to retain its color (red or green) during a 20s delay. During performance of the spatial WM task, cerebral activation trends were found in which DPFC exhibited stronger activation than did the VPFC, and posterior parietal cortex maintained higher delay activation than did frontal regions. These differences were less pronounced during performance of the non-spatial task. Additionally, incorrect trials generally elicited lower activations during the delay period than did trials ending with a correct response. Furthermore, NIRS data collected during the performance of a haptic WM task also appear to exhibit inter-regional differences in delay activation. The data thus suggest the presence of preferential cognitive processing between and within posterior and frontal cortical regions