TY - JOUR

T1 - Inverse problem and singularity of the integration kernel

AU - Gang, Hu

AU - Ning, Cun-Zheng

AU - Haken, H.

N1 - Funding Information:
The authors thank Dr. Chen for kindly informing them of his recent work and for directing the authors’ attention to the inverse problem, and thank Dr. Liu for showing them his recent work. G.H. was supported in part by the University of Stuttgart, and in part by the National Natural Foundation of China and the Nonlinear Science Project of China. C.Z.N. was supported by the DFG through SFB 329.

PY - 1995/9/11

Y1 - 1995/9/11

N2 - Many important problems in physics and other sciences can be formulated in terms of the inverse problem of type n(y) = ∝K(y ∥ x)g(x) dx, where g(x) is unknown. We show that this problem can be completely solved for a quite general class of kernel K(y ∥ x) by analytically dilating n(y) and K(y ∥ x) to the complex z plane, and by the analysis of the singularity of the dilated kernel K(z ∥ x). The formalism is also extended to multi-dimensional cases.

AB - Many important problems in physics and other sciences can be formulated in terms of the inverse problem of type n(y) = ∝K(y ∥ x)g(x) dx, where g(x) is unknown. We show that this problem can be completely solved for a quite general class of kernel K(y ∥ x) by analytically dilating n(y) and K(y ∥ x) to the complex z plane, and by the analysis of the singularity of the dilated kernel K(z ∥ x). The formalism is also extended to multi-dimensional cases.

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U2 - 10.1016/0375-9601(95)00544-D

DO - 10.1016/0375-9601(95)00544-D

M3 - Article

AN - SCOPUS:58149324876

VL - 205

SP - 130

EP - 136

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 2-3

ER -