Multipoint Formulas for Phase Recovering from Phaseless Scattering Data

R. G. Novikov

doi:10.1007/s12220-019-00329-6

Multipoint Formulas for Phase Recovering from Phaseless Scattering Data

R. G. Novikov

IEPT RAS

Research output: Contribution to journal › Article › peer-review

Abstract

We give formulas for phase recovering from appropriate monochromatic phaseless scattering data at 2n points in dimension d= 3 and in dimension d= 2. These formulas are recurrent and explicit and their precision is proportional to n. By this result we continue studies of Novikov (Bulletin des Sciences Mathématiques 139(8):923–936, 2015), where formulas of such a type were given for n= 1 , d≥ 2.

Original language	English
Pages (from-to)	1965-1991
Number of pages	27
Journal	Journal of Geometric Analysis
Volume	31
Issue number	2
DOIs	https://doi.org/10.1007/s12220-019-00329-6
Publication status	Published - 1 Feb 2021

Keywords

Helmholtz equation
Monochromatic scattering data
Phase recovering
Phaseless inverse scattering
Schrödinger equation

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10.1007/s12220-019-00329-6

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abstract = "We give formulas for phase recovering from appropriate monochromatic phaseless scattering data at 2n points in dimension d= 3 and in dimension d= 2. These formulas are recurrent and explicit and their precision is proportional to n. By this result we continue studies of Novikov (Bulletin des Sciences Math{\'e}matiques 139(8):923–936, 2015), where formulas of such a type were given for n= 1 , d≥ 2.",

keywords = "Helmholtz equation, Monochromatic scattering data, Phase recovering, Phaseless inverse scattering, Schr{\"o}dinger equation",

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AB - We give formulas for phase recovering from appropriate monochromatic phaseless scattering data at 2n points in dimension d= 3 and in dimension d= 2. These formulas are recurrent and explicit and their precision is proportional to n. By this result we continue studies of Novikov (Bulletin des Sciences Mathématiques 139(8):923–936, 2015), where formulas of such a type were given for n= 1 , d≥ 2.

KW - Helmholtz equation

KW - Monochromatic scattering data

KW - Phase recovering

KW - Phaseless inverse scattering

KW - Schrödinger equation

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ER -

Multipoint Formulas for Phase Recovering from Phaseless Scattering Data

Abstract

Keywords

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