- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 649848, 13 pages
On Generalized Localization of Fourier Inversion Associated with an Elliptic Operator for Distributions
1Institute of Mathematics, National University of Uzbekistan, Hodjaeva Street 29, Tashkent 100125, Uzbekistan
2Institute of Advanced Technology (ITMA), University Putra Malaysia, 43400 Serdang, Selangor, Malaysia
3Department of Civil Engineering, Faculty of Engineering, Geospatial, Information Science Center (GIS RC), University Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia
Received 24 May 2012; Accepted 29 June 2012
Academic Editor: Allaberen Ashyralyev
Copyright © 2012 Ravshan Ashurov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- V. Ii'in, “On a generalized interpretation of the principle of localization for Fourier series with respect to fundamental systems of functions,” Sibirskiĭ Matematičeskiĭ Žurnal, vol. 9, no. 5, pp. 1093–1106, 1968.
- P. Sjölin, “Regularity and integrability of spherical means,” Monatshefte für Mathematik, vol. 96, no. 4, pp. 277–291, 1983.
- A. Carbery and F. Soria, “Almost-everywhere convergence of Fourier integrals for functions in Sobolev spaces, and an -localisation principle,” Revista Matemática Iberoamericana, vol. 4, no. 2, pp. 319–337, 1988.
- A. Carbery and F. Soria, “Pointwise Fourier inversion and localisation in ,” The Journal of Fourier Analysis and Applications, vol. 3, supplement 1, pp. 847–858, 1997.
- A. Bastis, “Generalized localization of Fourier series with respect to the eigenfunctions of the laplace operator in the classes classes,” Litovskiĭ Matematicheskiĭ Sbornik, vol. 31, no. 3, pp. 387–405, 1991.
- A. Bastis, “The generalized localization principle for an N-fold Fourier integral,” Doklady Akademii Nauk SSSR, vol. 278, no. 4, pp. 777–778, 1984.
- A. Bastis, “On the generalized localization principle for an N-fold Fourier integral in the classes ,” Doklady Akademii Nauk SSSR, vol. 304, no. 3, pp. 526–529, 1989.
- R. Ashurov, A. Ahmedov, and A. Rodzi b. Mahmud, “The generalized localization for multiple Fourier integrals,” Journal of Mathematical Analysis and Applications, vol. 371, no. 2, pp. 832–841, 2010.
- F. J. González Vieli and E. Seifert, “Fourier inversion of distributions supported by a hypersurface,” The Journal of Fourier Analysis and Applications, vol. 16, no. 1, pp. 34–51, 2010.
- J. Vindas and R. Estrada, “Distributional point values and convergence of Fourier series and integrals,” The Journal of Fourier Analysis and Applications, vol. 13, no. 5, pp. 551–576, 2007.
- J. Vindas and R. Estrada, “On the order of summability of the Fourier inversion formula,” Analysis in Theory and Applications, vol. 26, no. 1, pp. 13–42, 2010.
- J. Vindas and R. Estrada, “On the support of tempered distributions,” Proceedings of the Edinburgh Mathematical Society 2, vol. 53, no. 1, pp. 255–270, 2010.
- Sh. A. Alimov, “On spectral decompositions of distributions,” Doklady Akademii Nauk, vol. 331, no. 6, pp. 661–662, 1993.
- Sh. A. Alimov and A. Rakhimov, “On the localization of spectral expansions of distributions,” Journal of Differential Equations, vol. 32, no. 6, pp. 792–802, 1996.
- Sh. A. Alimov and A. Rakhimov, “On the localization of spectral expansions of distributions in a closed domain,” Journal of Differential Equations, vol. 33, no. 1, pp. 80–82, 1997.
- Y. Egorov, Linear Differential Equations of Principal Type, Consultants Bureau, New York, NY, USA, 1986.
- E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, 1971.
- M. V. Fedoryuk, The Saddle-Point Method, Moscow, Russia, 1977.
- A. Garsia, Topics in Almost Everywhere Convergence, vol. 4 of Lectures in Advanced Mathematics, Markham Publishing Corporation, Chicago, Ill, USA, 1970.
- Sh. A. Alimov, R. Ashurov, and A. Pulatov, “Multiple Fourier series and Fourier integrals,” in Commutative Harmonic Analysis IV, vol. 42 of Encyclopaedia of Mathematical Sciences, pp. 1–97, Springer, 1992.