Il Nuovo Cimento (1943-1954)

, Volume 12, Issue 3, pp 335–350 | Cite as

Temperate distributions associated with the Klein-Gordon equation

  • A. Deprit


A distribution treatment is applied to the Klein-Gordon equation. The function Δ(x,t) is found to be theresolving distribution of the Klein-Gordon equation, considered as an evolution equation connected with the space convolution product. Δret(x,t) is theelementary kernel in the one-parameter algebra of operators which is associated with the Klein-Gordon differential operator. Finally\(\bar \Delta (x,t)\) is shown to be one of theelementary solutions of the Klein-Gordon equation, which is now regarded as a space-time convolution equation.


Si applica una distribuzione all’equazione di Klein-Gordon. Si trova che la funzione Δ(x,t) è ladistribuzione che risolve l’equazione di Klein-Gordon considerata come equazione di evoluzione connessa col prodotto di convoluzione spaziale. Δret(x,t) è ilnocciolo elementare nell’algebra degli operatori a un parametro, associato coll’operatore differenziale di Klein-Gordon. Finalmente, si dimostra che\(\bar \Delta (x,t)\) è una dellesoluzioni elementari dell’equazione di Klein-Gordon che si considera ora come un’equazione di convoluzione spazio-temporale.


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Copyright information

© Società Italiana di Fisica 1954

Authors and Affiliations

  • A. Deprit
    • 1
  1. 1.Christ’s CollegeCambridge

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