In this paper, we consider the numerical solutions of a fractional partial differential equation with Riesz space fractional derivatives (FPDE-RSFD) on a finite domain. Two kinds of FPDE-RSFD are considered: the Riesz fractional diffusion equation (RFDE) and the Riesz fractional advection-dispersion equation (RFADE). RFDE is obtained from the standard diffusion equation by replacing the secondo...

This paper presents a formal proof of the Riesz representation theorem in the PVS theorem prover. The Riemann Stieltjes integral was defined in PVS, and the theorem relies on this integral. In order to prove the Riesz representation theorem, it was necessary to prove that continuous functions on a closed interval are Riemann Stieltjes integrable with respect to any function of bounded variation...

this paper is an investigation of $l$-dual frames with respect to a function-valued inner product, the so called $l$-bracket product on $l^{2}(g)$, where g is a locally compact abelian group with a uniform lattice $l$. we show that several well known theorems for dual frames and dual riesz bases in a hilbert space remain valid for $l$-dual frames and $l$-dual riesz bases in $l^{2}(g)$.

A convergence in Riesz spaces is given axiomatically. A Bochner-type integral for Riesz space-valued functions is introduced and some Vitali and Lebesgue dominated convergence theorems are proved. Some properties and examples are investigated. A.M.S. SUBJECT CLASSIFICATION (2000): 28B15.

This paper is to construct Riesz wavelets with short support. Riesz wavelets with short support are of interests in both theory and application. In theory, it is known that a B-spline of order m has the shortest support among all compactly supported refinable functions with the same regularity. However, it remained open whether a Riesz wavelet with the shortest support and m vanishing moments c...

A Timoshenko beam equation with boundary feedback control is considered. By an abstract result on the Riesz basis generation for the discrete operators in the Hilbert spaces, we show that the closed-loop system is a Riesz system, that is, the sequence of generalized eigenvectors of the closed-loop system forms a Riesz basis in the state Hilbert space. 1. Introduction. The boundary feedback stab...

The paper is concerned with order-topological characterizations of topological Riesz spaces, in particular spaces of measurable functions, not containing Riesz isomorphic or linearly homeomorphic copies of c0 or `∞.

Analogous of Riesz potentials and Riesz transforms are defined and studied for the Dunkl transform associated with a family of weighted functions that are invariant under a reflection group. The L boundedness of these operators is established in certain cases.

We study the boundedness of Riesz transforms in L for p > 2 on a doubling metric measure space endowed with a gradient operator and an injective, ω-accretive operator L satisfying Davies-Gaffney estimates. If L is non-negative self-adjoint, we show that under a reverse Hölder inequality, the Riesz transform is always bounded on L for p in some interval [2, 2 + ε), and that L gradient estimates ...

Let (M, g) be a Riemannian manifold. The Riesz transform problem, namely giving conditions on p and on the manifold such that the operator d∆−1/2 – the so-called Riesz transform – is bounded on L, has recently undergone certain progresses. A pioneering result which goes back to 1985 is a theorem of D. Bakry [2] which asserts that if the Ricci curvature of M is non-negative, then the Riesz trans...