Third double-spectral function effects

It is shown for all graphs of the ‘strip approximation’ that the K ->3n decay amplitude obeys a Mandelstam double-dispersion relation. The double spectral function turns out to be complex and covers the whole physical domain, so that the Cini-Fubini approximation is no longer valid. Essential singularities are found on the border of the physical sheet. Double-dispersion relations in one energy and in the K mass are also derived.

Upper Bound for the Double Spectral Function in Potential Scattering

Journal of Mathematical Physics ◽

10.1063/1.1704315 ◽

1965 ◽

Vol 6 (4) ◽

pp. 637-643 ◽

Cited By ~ 17

Author(s):

D. Bessis

Keyword(s):

Spectral Function ◽

Upper Bound ◽

Potential Scattering ◽

Double Spectral Function

Singularities of the double spectral function in potential scattering theory

Il Nuovo Cimento A ◽

10.1007/bf02819605 ◽

1969 ◽

Vol 61 (4) ◽

pp. 638-643 ◽

Cited By ~ 2

Author(s):

O. Brander

Keyword(s):

Spectral Function ◽

Scattering Theory ◽

Potential Scattering ◽

Double Spectral Function

Upper Bound for the Double Spectral Function in Potential Scattering

Journal of the Physical Society of Japan ◽

10.1143/jpsj.20.643 ◽

1965 ◽

Vol 20 (5) ◽

pp. 643-648

Author(s):

Charles Thompson

Keyword(s):

Spectral Function ◽

Upper Bound ◽

Potential Scattering ◽

Double Spectral Function

Bound on the double spectral function for a class of Yukawian potentials

Nuclear Physics B ◽

10.1016/0550-3213(67)90075-2 ◽

1967 ◽

Vol 3 (3) ◽

pp. 195-206 ◽

Cited By ~ 1

Author(s):

M. Bertero ◽

H.J. Kreuzer

Keyword(s):

Spectral Function ◽

Double Spectral Function

l-dependence, singularities, and the double-spectral function

Il Nuovo Cimento A ◽

10.1007/bf02754537 ◽

1966 ◽

Vol 41 (2) ◽

pp. 266-269 ◽

Cited By ~ 1

Author(s):

J. J. Brehm

Keyword(s):

Spectral Function ◽

Double Spectral Function

Singularities of partial-wave amplitudes arising from the third double-spectral function

Il Nuovo Cimento ◽

10.1007/bf02821680 ◽

1964 ◽

Vol 31 (5) ◽

pp. 1079-1085 ◽

Cited By ~ 2

Author(s):

C. K. Jones ◽

V. L. Teplitz

Keyword(s):

Spectral Function ◽

Partial Wave ◽

The Third ◽

Double Spectral Function

Non-Debye Relaxations: Two Types of Memories and Their Stieltjes Character

Mathematics ◽

10.3390/math9050477 ◽

2021 ◽

Vol 9 (5) ◽

pp. 477

Author(s):

Katarzyna Górska ◽

Andrzej Horzela

Keyword(s):

Stochastic Processes ◽

Spectral Function ◽

Evolution Equations ◽

Memory Function ◽

Relaxation Phenomena ◽

Stieltjes Function ◽

Infinitely Divisible ◽

Spectral Functions ◽

Debye Relaxation ◽

Relaxation Functions

In this paper, we show that spectral functions relevant for commonly used models of the non-Debye relaxation are related to the Stieltjes functions supported on the positive semi-axis. Using only this property, it can be shown that the response and relaxation functions are non-negative. They are connected to each other and obey the time evolution provided by integral equations involving the memory function M(t), which is the Stieltjes function as well. This fact is also due to the Stieltjes character of the spectral function. Stochastic processes-based approach to the relaxation phenomena gives the possibility to identify the memory function M(t) with the Laplace (Lévy) exponent of some infinitely divisible stochastic processes and to introduce its partner memory k(t). Both memories are related by the Sonine equation and lead to equivalent evolution equations which may be freely interchanged in dependence of our knowledge on memories governing the process.