A stable method for the inversion of the Fourier transform in $ \mathbb{R}^{N} $

Leonede De Michele; Delfina Roux

A stable method for the inversion of the Fourier transform in $R^{N}$

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1993)

Volume: 4, Issue: 2, page 109-114
ISSN: 1120-6330

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Abstract

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A general method is given for recovering a function

f : R^{N} \to C

,

N \geq 1

, knowing only an approximation of its Fourier transform.

How to cite

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De Michele, Leonede, and Roux, Delfina. "A stable method for the inversion of the Fourier transform in $ \mathbb{R}^{N} $." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 4.2 (1993): 109-114. <http://eudml.org/doc/244112>.

@article{DeMichele1993,
abstract = {A general method is given for recovering a function $ f : \mathbb\{R\}^\{N\} \rightarrow C $, $ N \ge 1 $, knowing only an approximation of its Fourier transform.},
author = {De Michele, Leonede, Roux, Delfina},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Fourier transform; Inversion; Well posed; stable methods for recovering a function; approximation},
language = {eng},
month = {6},
number = {2},
pages = {109-114},
publisher = {Accademia Nazionale dei Lincei},
title = {A stable method for the inversion of the Fourier transform in $ \mathbb\{R\}^\{N\} $},
url = {http://eudml.org/doc/244112},
volume = {4},
year = {1993},
}

TY - JOUR
AU - De Michele, Leonede
AU - Roux, Delfina
TI - A stable method for the inversion of the Fourier transform in $ \mathbb{R}^{N} $
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1993/6//
PB - Accademia Nazionale dei Lincei
VL - 4
IS - 2
SP - 109
EP - 114
AB - A general method is given for recovering a function $ f : \mathbb{R}^{N} \rightarrow C $, $ N \ge 1 $, knowing only an approximation of its Fourier transform.
LA - eng
KW - Fourier transform; Inversion; Well posed; stable methods for recovering a function; approximation
UR - http://eudml.org/doc/244112
ER -

References

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DE MICHELE, L. - DI NATALE, M. - ROUX, D., Sharp properties of a régularisation method for inversion of Fourier series. Proceedings of the Meeting Trends in Functional Analysis and Approximation Theory. Atti Sem. Mat. Fis. Univ. Modena, 39, 1991, 253-267. Zbl0777.42003
DE MICHELE, L. - DI NATALE, M. - ROUX, D., Inverse Fourier transform. Rend. Mat. Acc. Lincei, s. 9, 1, 1990, 305-308. Zbl0711.42014 MR1096823
DE MICHELE, L. - DI NATALE, M. - ROUX, D., Inversion methods for Fourier transform. Rend. Accad. Naz. Sci. XL, Mem. Mat., 109°, 15, 1991, 125-136. Zbl0835.42007 MR1151574
DE MICHELE, L. - DI NATALE, M. - ROUX, D., On the effectiveness of some inversion methods for noisy Fourier series. In: S. P. SINGH (éd.), Proc. of NATO-ASI Meeting Approximation theory, spline functions and applications. Kluwer Acad. Publ., 1992, 255-267. Zbl0745.42001 MR1165972
DE MICHELE, L. - DI NATALE, M. - ROUX, D., Féjer kernels and noisy Fourier series. J. Comput. Appl. Math., to appear. Zbl0794.65097 MR1256009 DOI10.1016/0377-0427(93)90133-V
DI NATALE, M. - GOTUSSO, L. - PAVANI, R. - ROUX, D., Uniform approximation by Fourier polynomials with noisy coefficients. Ist. Lombardo Accad. Sci. Lett. Rend., A, 124, 1990, 147-155. Zbl0770.42004 MR1267855
DI NATALE, M. - GOTUSSO, L. - PAVANI, R. - ROUX, D., On the choice of the parameter in a method for inversion of Fourier series. Math. Comp., 58, 1992, 737-744. Zbl0770.42006 MR1122063 DOI10.2307/2153212
ROUX, D., On the inversion of noisy Fourier transforms. Proc. of 2nd International Conference in Functional Analysis and Appproximation Theory. Rend. Circ. Mat. Palermo, to appear. Zbl0824.42001 MR1295254
STEIN, E. M. - WEISS, G., Introduction to Fourier Analysis on Euclidean Spaces. Princeton Univ. Press, 1975. Zbl0232.42007 MR304972

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