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...

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 characterize, in terms of elementary properties, the abelian monoids which are direct limits of finite direct sums of monoids of the form ðZ=nZÞ t f0g (where 0 is a new zero element), for positive integers n. The key properties are the Riesz refinement property and the requirement that each element x has finite order, that is, ðnþ 1Þx 1⁄4 x for some positive integer n. Such monoids are neces...

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 ...

The method ot atomic decomposition of Besov and Lizorkin-Triebel function spaces is combined with basic ideas from the theory of singular integral operators and applied to the study of fractional integral and diierential operators (FIDO), of which the Riesz potential is considered in detail as a model example. The main new results are: characterization of the Riesz potential by an innnite-dimen...