Let H(B) denote the space of all holomorphic functions on the unit ball B of ℂⁿ. Let φ be a holomorphic self-map of B and g ∈ H(B) such that g(0) = 0. We study the integral-type operator $C_{\phi }^{g}f\left(z\right)={\int }_0^1\Re f\left(\phi \left(tz\right)\right)g\left(tz\right)dt/t$, f ∈ H(B). The boundedness and compactness of $C_{\phi }^g$ from Privalov spaces to Bloch-type spaces and little Bloch-type spaces are studied

An example of a nonzero σ-finite Borel measure μ with everywhere dense linear manifold ${}_{\mu }$ of admissible (in the sense of invariance) translation vectors is constructed in the Hilbert space ℓ₂ such that μ and any shift ${\mu }^{\left(a\right)}$ of μ by a vector $a\in \ell ₂{\setminus }_{\mu }$ are neither equivalent nor orthogonal. This extends a result established in [7].

Consideramos una clase de problemas de optimización que surgen en estimaciones de la densidad de datos en dimensión elevada a partir de proyecciones en subespacios de dimensión más baja. Los criterios que se usan para la selección óptima del modelo son máxima entropía y máxima verosimilitud. En cada caso nuestro planteamiento requiere estimadores de la densidad univariados y a este respecto exploramos el uso de modelos mezcla de densidades gaussianas y de estimadores de Parzen para los datos proyectados....

We show that in the space C[-1,1] there exists an orthogonal algebraic polynomial basis with optimal growth of degrees of the polynomials.

In this paper, we present an analytic definition for the relative torsion for flat C*-algebra bundles over a compact manifold. The advantage of such a relative torsion is that it is defined without any hypotheses on the flat C*-algebra bundle. In the case where the flat C*-algebra bundle is of determinant class, we relate it easily to the L^2 torsion as defined in [7],[5].

A certain class of Arens-Michael algebras having no non-zero injective topological ⨶-modules is introduced. This class is rather wide and contains, in particular, algebras of holomorphic functions on polydomains in ${ℂ}^n$, algebras of smooth functions on domains in ${ℝ}^n$, algebras of formal power series, and, more generally, any nuclear Fréchet-Arens-Michael algebra which has a free bimodule Koszul resolution.

A class of convex functions where the sets of subdifferentials behave like the unit ball of the dual space of an Asplund space is found. These functions, which we called Asplund functions also possess some stability properties. We also give a sufficient condition for a function to be an Asplund function in terms of the upper-semicontinuity of the subdifferential map.

A Banach space X is asymptotically symmetric (a.s.) if for some C < ∞, for all m ∈ ℕ, for all bounded sequences ${\left(x_j^i\right)}_{j=1}^{\infty }\subseteq X$, 1 ≤ i ≤ m, for all permutations σ of 1,...,m and all ultrafilters ₁,...,ₘ on ℕ, $li{m}_{n₁,₁}...li{m}_{nₘ,ₘ}\left|\right|{\sum }_{i=1}^m{x}_{n_i}^i\left|\right|\le Cli{m}_{n_{\sigma \left(1\right)}{,}_{\sigma \left(1\right)}}...li{m}_{n_{\sigma \left(m\right)}{,}_{\sigma \left(m\right)}}\left|\right|{\sum }_{i=1}^m{x}_{n_i}^i\left|\right|$. We investigate a.s. Banach spaces and several natural variations. X is weakly a.s. (w.a.s.) if the defining condition holds when restricted to weakly convergent sequences ${\left(x_j^i\right)}_{j=1}^{\infty }$. Moreover, X is w.n.a.s. if we restrict the condition further to normalized weakly null sequences. If X is a.s. then all spreading...