We consider a functional on the Wiener space which is smooth and not degenerated in Malliavin sense and we give a criterion for the strict positivity of the density, that we can use to state lower bounds as well. The results are based on the representation of the density in terms of the Riesz transform introduced in Malliavin and Thalmaier bib:[M.T] [16] and on the estimates of the Riesz transf...

In this paper, we consider linear space-time fractional reactiondiffusion equation with composite fractional derivative as time derivative and Riesz-Feller fractional derivative with skewness zero as space derivative. We apply Laplace and Fourier transforms to obtain its solution.

*Correspondence: [email protected] 3Faculty of Science and Technology, Tapee College, Surathani, 84000, Thailand Full list of author information is available at the end of the article Abstract In this paper, we obtain new Riesz representations of continuous linear maps associated with certain boundary value problems in the set of all closed bounded convex non-empty subsets of any Banach sp...

We examine condition numbers, preconditioners, and iterative methods for finite element discretizations of coercive PDEs in the context of the fundamental solvability result, the Lax-Milgram Lemma. Working in this Hilbert space context is justified because finite element operators are restrictions of infinite-dimensional Hilbert space operators to finite-dimensional subspaces. Moreover, useful ...

In this paper we use the standard terminology and notations of the Riesz spaces theory (see [2]). The Banach lattice of the continuous functions from a compact Hausdorff space into a Banach lattice E is denoted by C(K,E). If E = R then we write C(K) instead of C(K,E). 1 stands for the unit function in C(K). One version of the Banach–Stone theorem states that: Theorem 1. Let X and Y be compact H...

To represent the local orientation and energy of a 1-D image signal, many models of early visual processing employ bandpass quadrature filters, formed by combining the original signal with its Hilbert transform. However, representations capable of estimating an image signal's 2-D phase have been largely ignored. Here, we consider 2-D phase representations using a method based upon the Riesz tra...

In this summary we introduce a successful analogue of the classical Egoroff theorem for non-additive measures with values in a Riesz space having the asymptotic Egoroff property.