The Sokhotski–Plemelj theorem (Polish spelling is Sochocki) is a theorem in complex analysis, which helps in evaluating certain integrals. The real-line...

ordinary function within the space of tempered distributions. The Sokhotski–Plemelj theorem, important in quantum mechanics, relates the delta function to...

Josip Plemelj (December 11, 1873 – May 22, 1967) was a Slovene mathematician, whose main contributions were to the theory of analytic functions and the...

Kramers. In mathematics, these relations are known by the names Sokhotski–Plemelj theorem and Hilbert transform. Let χ ( ω ) = χ 1 ( ω ) + i χ 2 ( ω ) {\displaystyle...

the function f ( z ) {\displaystyle f(z)} is meromorphic, the Sokhotski–Plemelj theorem relates the principal value of the integral over C with the mean-value...

other mathematicians. His doctoral thesis contains the famous Sokhotski–Plemelj theorem. From 1868 Sochotcki lectured at the St Petersburg university...

equation Redfield equation Open quantum system Quantum jump method Sokhotski–Plemelj theorem § Heitler function Breuer, Heinz-Peter; Petruccione, F. (2002)...

Rouché's theorem Bromwich integral Morera's theorem Mellin transform Kramers–Kronig relation, a. k. a. Hilbert transform Sokhotski–Plemelj theorem Exponential...

infinity. As for the first integral, one can use one version of the Sokhotski–Plemelj theorem for integrals over the real line: for a complex-valued function...

distributions, noting that the equation xf(x) = 1 has the solution (see Sokhotski–Plemelj theorem) f ( x ) = 1 x ± i ε = 1 x ∓ i π δ ( x ) , {\displaystyle f(x)={\frac...

evaluated using a partial fraction expansion and an evaluation using the Sokhotski–Plemelj formula: ∫ L ∗ d τ 1 τ 1 − t = ∫ L ∗ d τ 1 τ 1 − t = π   i   . {\displaystyle...

is unique (an easy application of Liouville's theorem (complex analysis)), the Sokhotski–Plemelj theorem gives the solution. We get log ⁡ M = 1 2 π i ∫...

convolution type. The Hilbert transform satisfies the jump relations of Plemelj and Sokhotski, which express the original function as the difference between the...