A stable method for the inversion of the Fourier transform in
Leonede De Michele; Delfina Roux
- Volume: 4, Issue: 2, page 109-114
- ISSN: 1120-6330
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topDe 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
top- 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. Zbl0711.42014MR1096823
- 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. Zbl0835.42007MR1151574
- 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. Zbl0745.42001MR1165972
- DE MICHELE, L. - DI NATALE, M. - ROUX, D., Féjer kernels and noisy Fourier series. J. Comput. Appl. Math., to appear. Zbl0794.65097MR1256009DOI10.1016/0377-0427(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. Zbl0770.42004MR1267855
- 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. Zbl0770.42006MR1122063DOI10.2307/2153212
- 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. Zbl0824.42001MR1295254
- STEIN, E. M. - WEISS, G., Introduction to Fourier Analysis on Euclidean Spaces. Princeton Univ. Press, 1975. Zbl0232.42007MR304972
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