This paper presents a functional-level detector simulation technique which is based on the Hilbert Transforms and can be used together with the Discrete Technique. AM-detector simulation as well as its constrains, improvements and validation has been discussed in detail. It has been shown that the RC-circuit at the detector output should be ignored during the simulation. The technique proposed ...

The notion of monotonic independence, introduced by N. Muraki, is considered in a more general frame, similar to the construction of operatorvalued free probability. The paper presents constructions for maps with similar properties to the H and K transforms from the literature, semi inner-product bimodule analogues for the monotone and weakly monotone product of Hilbert spaces, an ad-hoc versio...

The generalized Beurling–Ahlfors operator S on L(R; Λ), where Λ := Λ(R) is the exterior algebra with its natural Hilbert space norm, satisfies the estimate ‖S‖L (Lp(Rn;Λ)) ≤ (n/2 + 1)(p ∗ − 1), p∗ := max{p, p′}. This improves on earlier results in all dimensions n ≥ 3. The proof is based on the heat extension and relies at the bottom on Burkholder’s sharp inequality for martingale transforms.

In this paper we present an explicit method of radial basis function approximation over Rn, using the Green's function for Laplace's equation. We prove convergence of the scheme for all functions that are continuous and of compact support. Interesting variants of formul result, in cases when lower dimensional formul are used to construct higher dimensional ones, and in cases of periodic functio...

Preface These lecture notes present elements of Hilbert space and the theory of linear operators on Hilbert space, and their application to integral equations. Chapter 1 reviews vector spaces: bases, subspaces, and linear transforms. Chapter 2 covers the basics of Hilbert space. It includes the concept of Ba-nach space and Hilbert space, orthogonality, complete orthogonal bases, and Riesz repre...

The major task in quantum control theory is to find an external field that transforms the system from one state to another or executes a predetermined unitary transformation. We investigate the difficulty of computing the control field as the size of the Hilbert space is increased. In the models studied the controls form a small closed subalgebra of operators. Complete controllability is obtain...

In this paper, we studied q-analogue of Sturm–Liouville boundary value problem on a finite interval having discontinuity in an interior point. We proved that the q-Sturm–Liouville is self-adjoint modified Hilbert space. investigated spectral properties eigenvalues and eigenfunctions problem. shown are form complete system. Finally, sampling theorem for integral transforms whose kernels basic fu...