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A multiplier theorem for the Hankel transform.

Rafal Kapelko (1998)

Revista Matemática Complutense

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

Characterization of Bessel sequences.

M. Laura Arias, Gustavo Corach, Miriam Pacheco (2007)

Extracta Mathematicae

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.

Regularity of domains of parameterized families of closed linear operators

Teresa Winiarska, Tadeusz Winiarski (2003)

Annales Polonici Mathematici

The purpose of this paper is to provide a method of reduction of some problems concerning families A t = ( A ( t ) ) t of linear operators with domains ( t ) t to a problem in which all the operators have the same domain . To do it we propose to construct a family ( Ψ t ) t of automorphisms of a given Banach space X having two properties: (i) the mapping t Ψ t is sufficiently regular and (ii) Ψ t ( ) = 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 memristive circuits

Artur Sowa (2012)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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...

The Heisenberg uncertainty relation in harmonic analysis on p -adic numbers field

Cui Minggen, Zhang Yanying (2005)

Annales mathématiques Blaise Pascal

In this paper, two important geometric concepts–grapical center and width, are introduced in p -adic numbers field. Based on the concept of width, we give the Heisenberg uncertainty relation on harmonic analysis in p -adic numbers field, that is the relationship between the width of a complex-valued function and the width of its Fourier transform on p -adic numbers field.

Weyl-Heisenberg frame in p -adic analysis

Minggen Cui, Xueqin Lv (2005)

Annales mathématiques Blaise Pascal

In this paper, we establish an one-to-one mapping between complex-valued functions defined on R + { 0 } and complex-valued functions defined on p -adic number field Q p , and introduce the definition and method of Weyl-Heisenberg frame on hormonic analysis to p -adic anylysis.

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