On Discrete Variables whose Sum is Absolutely Continuous

On Absolutely Continuous Transformations

From Discrete to Absolutely Continuous Solutions of Indeterminate Moment Problems

We consider well-known families of discrete solutions to indeterminate moment problems and show how they can be used in a simple way to generate absolutely continuous solutions to the same moment problems. The following cases are considered: log-normal, generalized Stieltjes-Wigert, q-Laguerre and discrete q-Hermite II.

The Absolutely Continuous Spectrum of Discrete Canonical Systems

We prove that if the canonical system J(yn+1 − yn) = zHnyn has absolutely continuous spectrum of a certain multiplicity, then there is a corresponding number of linearly independent solutions y which are bounded in a weak sense.

O ct 1 99 4 Cardinal invariants concerning functions whose sum is almost continuous

Cardinal invariants concerning functions whose sum is almost continuous. Abstract Let A stand for the class of all almost continuous functions from R to R and let A(A) be the smallest cardinality of a family F ⊆ R R for which there is no g: R → R with the property that f + g ∈ A for all f ∈ F. We define cardinal number A(D) for the class D of all real functions with the Darboux property similar...

Kernel Machines for Continuous and Discrete Variables

Kernel Machines, such as Support Vector Machines, have been frequently used, with considerable success, in situations in which the input variables were real values. Lately, these methods have also been extended to deal with discrete data such as string characters, microarray gene expressions, biosequences, etc. In this contribution we describe a new kernel allowing kernel machines to be applied...