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

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Résumé

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.

langue originale	Anglais
Pages (de - à)	1965-1991
Nombre de pages	27
journal	Journal of Geometric Analysis
Volume	31
Numéro de publication	2
Les DOIs	https://doi.org/10.1007/s12220-019-00329-6
état	Publié - 1 févr. 2021

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10.1007/s12220-019-00329-6

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title = "Multipoint Formulas for Phase Recovering from Phaseless Scattering Data",

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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DO - 10.1007/s12220-019-00329-6

M3 - Article

AN - SCOPUS:85076572965

SN - 1050-6926

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SP - 1965

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JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 2

ER -

Multipoint Formulas for Phase Recovering from Phaseless Scattering Data

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