and Applied Analysis 3 Remark 1.5. If f x /x is increasing on I and 1.6 holds, then the Petrović-type functional P1 is nonnegative, that is, inequality 1.4 is valid. Conversely, if f x /x is increasing on I and conditions as in 1.7 are fulfilled, then relation 1.5 holds. In order to define another Petrović-type functional, we cite the following Petrović-type inequality involving a convex functi...

a general notion of completely monotone functionals on an ordered banach algebra b into a proper h*-algebra a with an integral representation for such functionals is given. as an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. a generalized version of bochner’s theorem on foundation se...

We consider exponential functionals of a multi-dimensional Brownian motion with drift, defined via a collection of linear functionals. We give a characterisation of the Laplace transform of their joint law as the unique bounded solution, up to a constant factor, to a Schrödinger-type partial differential equation. We derive a similar equation for the probability density. We then characterise al...

We consider minimizers of linear functionals of the type

We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals. We give a semidirect product decomposition for an abelian groupoid. This is done through a matched pair and leads to a C*-diagonal (for a special case). We use this decomposition to study ...

In this paper, we provide UL-type and LU -type RG-factorizations for an irreducible continuous-time level-dependent quasi-birth-and-death (QBD) process with either finitely-many levels or infinitely-many levels, and then apply theRG-factorizations to solve a type of linear QBD-equations, which is always crucial for analyzing a stochastic model described as a QBD process. Based on the results ob...

The purpose of this paper is to present to the Inverse Problems community some recent results regarding \nonsmooth", \edge preserving" regularization methods. Emphasis is placed on the penalized least squares (Tikhonov) regularization approach with penalty functionals of total variation type, although other nonquadratic penalty functionals are brieey discussed.