### A multiplier theorem for the Hankel transform.

Riesz function technique is used to prove a multiplier theorem for the Hankel transform, analogous to the classical Hörmander-Mihlin multiplier theorem (Hörmander (1960)).

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Riesz function technique is used to prove a multiplier theorem for the Hankel transform, analogous to the classical Hörmander-Mihlin multiplier theorem (Hörmander (1960)).

Let H be a separable Hilbert space, L(H) be the algebra of all bounded linear operators of H and Bess(H) be the set of all Bessel sequences of H. Fixed an orthonormal basis E = {ek}k∈N of H, a bijection αE: Bess(H) → L(H) can be defined. The aim of this paper is to characterize α-1E (A) for different classes of operators A ⊆ L(H). In particular, we characterize the Bessel sequences associated to injective operators, compact operators and Schatten p-classes.

The purpose of this paper is to provide a method of reduction of some problems concerning families ${A}_{t}={\left(A\left(t\right)\right)}_{t\in}$ of linear operators with domains ${{(}_{t})}_{t\in}$ to a problem in which all the operators have the same domain . To do it we propose to construct a family ${\left({\Psi}_{t}\right)}_{t\in}$ of automorphisms of a given Banach space X having two properties: (i) the mapping $t\mapsto {\Psi}_{t}$ is sufficiently regular and (ii) ${\Psi}_{t}\left(\right){=}_{t}$ for t ∈ . Three effective constructions are presented: for elliptic operators of second order with the Robin boundary condition with a parameter;...

Signals generated in circuits that include nano-structured elements typically have strongly distinct characteristics, particularly the hysteretic distortion. This is due to memristance, which is one of the key electronic properties of nanostructured materials. In this article, we consider signals generated from a memrsitive circuit model. We demonstrate numerically that such signals can be efficiently represented in certain custom-designed nonorthogonal bases. The proposed method ensures that the...

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