We construct a new method for approximating Hilbert transforms and their inverse throughout the complex plane. Both problems can be formulated as Riemann–Hilbert problems via Plemelj’s lemma. Using this framework, we rederive existing approaches for computing Hilbert transforms over the real line and unit interval, with the added benefit that we can compute the Hilbert transform in the complex ...

In this paper we view some fundamentals of the theory of Hilbert C-modules and examine some ways in which Hilbert C-modules differ from Hilbert spaces. ∗2000 Mathematics Subject Classification. 46L08.

Hilbert words correspond to finite approximations of the Hilbert space filling curve. The Hilbert infinite word H is obtained as the limit of these words. It gives a description of the Hilbert (infinite) curve. We give a uniform tag-system to generate automatically H and, by showing that it is almost cube-free, we prove that it cannot be obtained by simply iterating a morphism.

Hilbert words correspond to finite approximations of the Hilbert space filling curve. The Hilbert infinite word H is obtained as the limit of these words. It gives a description of the Hilbert (infinite) curve. We give a uniform tag-system to generate automatically H and, by showing that it is almost cube-free, we prove that it cannot be obtained by simply iterating a morphism.

In this paper, a new notion of frames is introduced: $ast$-operator frame as generalization of $ast$-frames in Hilbert $C^{ast}$-modules introduced by A. Alijani and M. A. Dehghan cite{Ali} and we establish some results.

In Hilbert space L2(Rn), we prove the equivalence between the mod-ulus of smoothness and the K-functionals constructed by the Sobolev space cor-responding to the Fourier transform. For this purpose, Using a spherical meanoperator.

We exemplify the way the rigged Hilbert space deals with the Lippmann-Schwinger equation by way of the spherical shell potential. We explicitly construct the Lippmann-Schwinger bras and kets along with their energy representation, their time evolution and the rigged Hilbert spaces to which they belong. It will be concluded that the natural setting for the solutions of the Lippmann-Schwinger equ...

Steingrı́msson (2001) showed that the chromatic polynomial of a graph is the Hilbert function of a relative StanleyReisner ideal. We approach this result from the point of view of Ehrhart theory and give a sufficient criterion for when the Ehrhart polynomial of a given relative polytopal complex is a Hilbert function in Steingrı́msson’s sense. We use this result to establish that the modular and ...

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 ...