On Existence and Uniqueness Theorems Concerning the H-Matrix of Radiative Transfer

Siewert, C. E.; Burniston, E. E.

doi:10.1086/151525

Cited by 24 publications

(4 citation statements)

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“…The solution of such an equation is well known. [13] The solution of Eq. This requires that Tða, uÞ AE i ða=2Þu does not vanish in [0, 1], which is the case.…”

Section: Cauchy Integral Equations and Their Solution On The Cut [0 1]mentioning

confidence: 99%

“…This function has been previously studied by Mullikin, [5] Carlstedt and Mullikin, [7] Case and Zweifel, [3] and Siewert and Burniston [13] for different models of scattering. Mullikin's notations are adopted hereafter.…”

Section: The N-functionmentioning

confidence: 99%

“…The N-function satisfies three fundamental equations, which were established in Cn0, 1 in the sixties [3,5,7,13]. We write hereafter the corresponding equations on the cut [0, 1] with the help of the Plemelj's formulae.…”

mentioning

confidence: 99%

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RADIATIVE TRANSFER IN PLANE-PARALLEL MEDIA AND CAUCHY INTEGRAL EQUATIONS. I. THEN-FUNCTION

Rutily

Bergeat

2002

Transport Theory and Statistical Physics

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We return to the Cauchy integral equations encountered in transfer problems when formulated in plane-parallel media. Light scattering is assumed isotropic for simplicity. The analytical properties of the classical N-function are reviewed. This function is sectionally analytic in the complex plane cut along the segment [0, 1]. Its domain is extended to the whole complex plane, except at þ1 where it diverges. We write down the functional relations satisfied by N outside [0, 1] and extend them on the cut with the help of Plemelj's formulae. This article is an introduction to a revisited derivation of the functions H and X, Y of plane-parallel media from the singular integral equations they satisfy.

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“…The solution of such an equation is well known. [13] The solution of Eq. This requires that Tða, uÞ AE i ða=2Þu does not vanish in [0, 1], which is the case.…”

Section: Cauchy Integral Equations and Their Solution On The Cut [0 1]mentioning

confidence: 99%

Section: The N-functionmentioning

confidence: 99%

See 1 more Smart Citation

RADIATIVE TRANSFER IN PLANE-PARALLEL MEDIA AND CAUCHY INTEGRAL EQUATIONS. I. THEN-FUNCTION

Rutily

Bergeat

2002

Transport Theory and Statistical Physics

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“…For a special kernel encountered in a certain type of transfer problem in volving polarized light, Siewert and co-workers have overcome the difficulties with half-range completeness (187,188) and have obtained extensive analytical and numerical solutions (189)(190)(191).…”

Section: Continuous Speedmentioning

confidence: 99%