Differential problems with the Riesz derivative in space are widely used to model anomalous diffusion. Although Riesz–Caputo is more suitable for modeling real phenomena, there few examples literature where numerical methods solve such differential problems. In this paper, we propose approximate of a given function cubic spline. As far as aware, first time that splines have been context derivat...

This paper aims to study fuzzy order bounded linear operators between two Riesz spaces. Two lattice operations are defined make the set of all as a space when codomain is Dedekind complete. As special case, separation property in dual studied. Furthermore, we studied norms compatible with ordering (fuzzy norm space) and discussed relation topological locally convex solid space.

Given a functional defined on a nonempty subset of an Archimedean Riesz space with unit, necessary and sufficient conditions are obtained for the existence of a (convex or concave) niveloid that extends the functional to the entire space. In the language of mathematical finance, this problem is equivalent to the one of verifying if the policy adopted by a regulator is consistent with monetary r...

The classical theorems of Riesz [l] on compact operators have been extended by Leray [2] and Williamson [3] to the context of topological linear spaces. Ringrose [4] has shown that if an operator on such a space is compact, the square of its adjoint is also compact, where the topology on the dual space is that of uniform convergence on bounded sets. Thus if an operator is continuous and some po...

On the n-dimensional hypercube, for given k ∈ N, wavelet Riesz bases are constructed for the subspace of divergence-free vector fields of the Sobolev space Hk((0, 1)n)n with general homogeneous Dirichlet boundary conditions, including slip or no-slip boundary conditions. Both primal and suitable dual wavelets can be constructed to be locally supported. The construction of the isotropic wavelet ...

In this paper, we investigate the existence of nontrivial solutions in Bessel Potential space for nonlinearfractional Schrödinger-Poisson system involving distributional Riesz fractional derivative. By using themountain pass theorem combination with perturbation method, prove solutions.

Let H be a Hilbert space and E a Banach space. In this note we present a sufficient condition for an operator R : H → E to be γ–radonifying in terms of Riesz sequences in H . This result is applied to recover a result of Lutz Weis and the second named author on the R-boundedness of resolvents, which is used to obtain a Datko-Pazy type theorem for the stochastic Cauchy problem. We also present s...

On the n-dimensional hypercube, for given k ∈ N, biorthogonal wavelet Riesz bases are constructed for the subspace of divergence-free vector fields of the Sobolev space Hk((0, 1)n)n with general homogeneous Dirichlet boundary conditions, including slip or no-slip boundary conditions. Both primal and dual wavelets can be constructed to be locally supported. The construction of the isotropic wave...

In this paper, we study the two weight commutators theorem of Riesz potential on an arbitrary homogeneous group H dimension N. Moreover, in accordance with results Euclidean space, acquire quantitative weighted bound group.

We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions, one being affinely dependent on the eigen-parameter. We give sufficient conditions under which a basis of each root subspace for this Sturm-Liouville problem can be selected so that the union of all these bases constitutes a Riesz basis of a corresponding weighted Hilbert space.