Generalizzazione di una formola del Källen

Susana Elena Trione

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1972)

  • Volume: 52, Issue: 2, page 115-119
  • ISSN: 0392-7881

Abstract

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Let n and k be fixed integers; n even ≥ 4 ; 1 ≤ k ≤ n - 2 2 . Let f ⁢ ( t ) , 0 ≤ t < ∞ , be differentiable and such that ∫ 0 ∞ | f ⁢ ( t ) | ⁢ t ( n - 2 ⁢ k ) / 2 ⁢ 𝑑 t < ∞ . We prove that, under these conditions, the integral equation (2) admits the solution (4). In the particular case n = 4 , k = 1 (which is important in the quantum theory of fields) the reciprocal formulae (2) and (4) have already been obtained (on the basis of heuristical considerations) by Källen [1].

How to cite

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Trione, Susana Elena. "Generalizzazione di una formola del Källen." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 52.2 (1972): 115-119. <http://eudml.org/doc/295775>.

@article{Trione1972,
author = {Trione, Susana Elena},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
language = {ita},
month = {2},
number = {2},
pages = {115-119},
publisher = {Accademia Nazionale dei Lincei},
title = {Generalizzazione di una formola del Källen},
url = {http://eudml.org/doc/295775},
volume = {52},
year = {1972},
}

TY - JOUR
AU - Trione, Susana Elena
TI - Generalizzazione di una formola del Källen
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1972/2//
PB - Accademia Nazionale dei Lincei
VL - 52
IS - 2
SP - 115
EP - 119
LA - ita
UR - http://eudml.org/doc/295775
ER -

References

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  1. KÄLLEN, G., Rélations de dispersion et particules élémentaires, Paris, Hermann, 1960, pp. 412-413- 
  2. KÄLLEN, G. and TOLL, J., Integral representations for the vacuum expectation value of three scalar local fields, «Helvetica Physica Acta», 33, 753-772 (1960). MR127244
  3. SVENSSON, Y., Relation between Fourier transform and integral representation for the two and three point functions, «Nuclear Physics», 39, 198-219 (1962). Zbl0108.42004MR148371

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