Aling of electromagnetic form factors and the behavior of their Fourier transforms in the neighborhood of the light cone

Zav'yalov, B. I.

doi:10.1007/bf01037255

Cited by 36 publications

(16 citation statements)

References 3 publications

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“…The Lojasiewicz notion admits a natural generalization, the quasiasymptotic behavior, which may be used to describe pointwise asymptotic properties of distributions as well as asymptotic properties at infinity. The quasiasymptotics were introduced by Zavialov [54] as a result of his investigations in quantum field theory, and further developed by him, Vladimirov and Drozhzhinov (see [7]- [10], [47]- [50]). Later on, the theory had its main developments within the study of integral transforms, convolution equations, partial differential equations, multiresolution expansions and Abelian and Tauberian theory (see [7]- [10], [13]- [15], [30]- [33], [38], [47]- [53]).…”

Section: Introductionmentioning

confidence: 99%

Tauberian Theorems for the Wavelet Transform

Vindas

Pilipović

Rakić

2010

J Fourier Anal Appl

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Abstract. We make a complete wavelet analysis of asymptotic properties of distributions. The study is carried out via Abelian and Tauberian type results, connecting the boundary asymptotic behavior of the wavelet transform with local and non-local quasiasymptotic properties of elements in the Schwartz class of tempered distributions. Our Tauberian theorems are full characterizations of such asymptotic properties. We also provide precise wavelet characterizations of the asymptotic behavior of elements in the dual of the space of highly time-frequency localized functions over the real line. For the use of the wavelet transform in local analysis, we study the problem of extensions of distributions initially defined on R \ {0} to R; in this extension problem, we explore the asymptotic properties of extensions of a distribution having a prescribed asymptotic behavior. Our results imply intrinsic properties of functions and measures as well, for example, we give a new proof of the classical Littlewood Tauberian theorem for power series.

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Section: Introductionmentioning

confidence: 99%

Tauberian Theorems for the Wavelet Transform

Vindas

Pilipović

Rakić

2010

J Fourier Anal Appl

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“…We have listed Ž w x . some of them in the references see 2, 4᎐9, 13᎐20, 22,23 . w x Recently Estrada and Kanwal 5᎐9 published interesting results in this direction which have found applications in various fields of pure and applied mathematics, physics, and engineering.…”

Section: Introductionmentioning

confidence: 99%

Taylor Expansion for Generalized Functions

Stanković

1996

Journal of Mathematical Analysis and Applications

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“…The main subject of this section are the so-called quasiasymptotic behaviors of distributions at infinity and the origin which we now proceed to define [9,11,12,16,24,25,29]. There are several definitions in the literature, let us start with the one from [11,12].…”

Section: The Structure Of Quasiasymptoticsmentioning

confidence: 99%

“…The concept of the quasiasymptotic behavior of distributions was introduced by B. I. Zavialov for tempered distributions in [29] and was studied comprehensively in [24]. Later this concept was slightly reformulated in [11,12].…”

Section: Introductionmentioning

confidence: 99%

“…The quasiasymptotics of distributions have shown to be of importance in several areas such as mathematical physics [24,29], abelian and tauberian theory of integral transforms [16,24,25], asymptotic behavior of solutions of partial differential equations [5,8,21,24,28] and summability of trigonometric series and integrals [6,8,21,22,26,27].…”

Section: Introductionmentioning

confidence: 99%

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The structure of quasiasymptotics of Schwartz distributions

Vindas

2010

Linear and Non-Linear Theory of Generalized Functions and Its Applications

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Abstract. In this article complete characterizations of quasiasymptotic behaviors of Schwartz distributions are presented by means of structural theorems. The cases at infinity and the origin are both analyzed. Special attention is paid to the quasiasymptotic of degree -1 and it is shown how the structural theorem can be used to study Cesàro and Abel summability of trigonometric series and integrals. Further properties of quasiasymptotics at infinity are discussed, the author presents a condition over test functions which allows one to evaluate them at the quasiasymptotic, these test functions are in bigger spaces than S. An extension of the structural theorems for quasiasymptotics is given, the author studies a structural characterization of the behavior f (λx) = O(ρ(λ)) in D , where ρ is a regularly varying function.

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Aling of electromagnetic form factors and the behavior of their Fourier transforms in the neighborhood of the light cone

Cited by 36 publications

References 3 publications

Tauberian Theorems for the Wavelet Transform

Tauberian Theorems for the Wavelet Transform

Taylor Expansion for Generalized Functions

The structure of quasiasymptotics of Schwartz distributions

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