Decay of Fourier transforms and summability of eigenfunction expansions
Luca Brandolini; Leonardo Colzani
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2000)
- Volume: 29, Issue: 3, page 611-638
- ISSN: 0391-173X
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topBrandolini, Luca, and Colzani, Leonardo. "Decay of Fourier transforms and summability of eigenfunction expansions." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 29.3 (2000): 611-638. <http://eudml.org/doc/84421>.
@article{Brandolini2000,
author = {Brandolini, Luca, Colzani, Leonardo},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {3},
pages = {611-638},
publisher = {Scuola normale superiore},
title = {Decay of Fourier transforms and summability of eigenfunction expansions},
url = {http://eudml.org/doc/84421},
volume = {29},
year = {2000},
}
TY - JOUR
AU - Brandolini, Luca
AU - Colzani, Leonardo
TI - Decay of Fourier transforms and summability of eigenfunction expansions
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2000
PB - Scuola normale superiore
VL - 29
IS - 3
SP - 611
EP - 638
LA - eng
UR - http://eudml.org/doc/84421
ER -
References
top- [1] S.A. Alimov - V.A. Il'in - E.M. Nikishin, Convergence problems of multiple trigonometric series and spectral decompositions, I, II, Russian Math. Surveys31 (1976), 29-86, 32 (1977), 115-139. Zbl0376.42002
- [2] P. Bérard, On the wave equation on a manifold without conjugate points, Math. Z.155 (1977), 249-276. Zbl0341.35052MR455055
- [3] P. Bérard, Riesz means on Riemannian manifolds, Amer. Math. Soc. Proc. Symp. Pure Math. XXXVI (1980), 1-12. Zbl0443.58023MR573426
- [4] S. Bochner, Summation of multiple Fourier series by spherical means, Trans. Amer. Math. Soc.40 (1936), 175-207. Zbl0015.15702MR1501870JFM62.0293.03
- [5] L. Brandolini - L. Colzani, Localization and convergence of eigenfunction expansions, J. Fourier Anal. Appl.5 (1999), 431-447. Zbl0938.42015MR1755098
- [6] L. Brandolini - L. Colzani - G. Travaglini, Average decay of Fourier transforms and integer points in polyhedra, Ark. Mat.35 (1997), 253-275. Zbl0937.11043MR1478780
- [7] L. Colzani - M. Vignati, The Gibbs phenomenon for multiple Fourier integrals, J. Approx. Th.80 (1995), 119-131. Zbl0815.42008MR1308597
- [8] L. De Michele - D. Roux, Approximate units and Gibbs phenomenon, Boll. Un. Mat. Ital. A (7) (1997), 739-746. Zbl0898.42002MR1489045
- [9] L. De Michele - D. Roux, The Gibbs phenomenon for L1 loc kernels, J. Approx. Th.100 (1999), 144-156. Zbl0953.42006MR1710557
- [10] L. De Michele - D. Roux, The Gibbs phenomenon for multiple Fourier integrals and series: restriction theorems, Atti Sem. Mat. Fis. Univ. Modena46 (1998), 351-360. Zbl0916.42008MR1645726
- [11] G.H. Hardy, On the expression of a number as a sum of two squares, Quart. J. Math.46 (1915), 263-283. Zbl45.1253.01JFM45.1253.01
- [12] E. Hlawka, Uber Integrale auf convexen Korpen, I & II, Monats. Math. 54 (1950), 1-36, 81-99. Zbl0036.30902MR37003
- [13] C. Herz, Fourier transform related to convex sets, Ann. of Math.75 (1962), 81-92. Zbl0111.34803MR142978
- [14] L. Hörmander, On the Riesz means of spectral functions and eigenfunction expansions for elliptic differential operators, In: "Some recent advances in the basic sciences", Yeshiva University1966, pp. 155-202. MR257589
- [15] L. Hörmander, The spectral function of an elliptic operator, Acta Math. 121 (1968), 193-218. Zbl0164.13201MR609014
- [16] L. Hörmander, "The analysis of linear partial differential operators", I, II, III, IV, Springer Verlag, 1985-1985. Zbl0830.60006
- [17] J.P. Kahane, Le phénomène de Pinsky et la géométrie des surfaces, C. R. Acad. Sci. Paris321 (1995), 1027-1029. Zbl0841.42004MR1360566
- [18] D.G. Kendall, On the number of lattice points inside a random oval, Quart. J. Math. Oxford19 (1948), 1-26. Zbl0031.11201MR24929
- [19] C. Meaney, On almost-everywhere convergent eigenfunction expansions of the Laplace-Beltrami operator, Math. Proc. Cambridge Philos. Soc. 92 (1982), 129-131. Zbl0495.58030MR662968
- [20] M.A. Pinsky, Pointwise Fourier inversion and related eigenfunction expansions, Comm. Pure Appl. Math.47 (1994), 653-681. Zbl0802.42010MR1278348
- [21] M.A. Pinsky, Fourier inversion in the piecewise smooth category, In: "Fourier Analysis, analytic and geometric aspects", W. O. Bray - P. S. Milojevic' - C. V. Stanojevic' (eds.), Marcel Dekker (1994). Zbl0815.42007MR1277831
- [22] M.A. Pinsky - M. Taylor, Pointwise Fourier inversion: a wave equation approach, J. Fourier Anal. Appl.3 (1997), 647-703. Zbl0901.42008MR1481629
- [23] A.N. Podkorytov, The asymptotic of Fourier transform of a convex curve, Vestnik Leningr. Univ. Mat.24 (1991), 57-65. Zbl0741.42012MR1166380
- [24] C.D. Sogge, Concerning the Lp norm of spectral clusters for second order elliptic differential operators on compact manifolds, J. Funct. Anal.77 (1988), 123-134. Zbl0641.46011MR930395
- [25] C.D. Sogge, On the convergence of Riesz means on compact manifolds, Ann. of Math.126 (1987), 439-447. Zbl0653.35068MR908154
- [26] E.M. Stein - G. Weiss, "Introduction to Fourier analysis on Euclidean spaces", Princeton University Press, 1971. Zbl0232.42007MR304972
- [27] M.E. Taylor, Pointwise Fourier inversion on tori and other compact manifolds, J. Fourier Anal. Appl.5 (1999), 449-463. Zbl0938.42007MR1755099
- [28] M.E. Taylor, Pointwise Fourier inversion - an addendum, Proc. Amer. Math. Soc., to appear. Zbl0967.42006MR1825908
- [29] M.E. Taylor, The Dirichlet-Jordan test and multidimensional extensions, Proc. Amer. Math. Soc., to appear. Zbl0969.42006MR1709767
- [30] M.E. Taylor, Eigenfunction expansions and the Pinsky phenomenon on compact manifolds, preprint. Zbl1065.58023MR1845101
- [31] A. Torlaschi, Sviluppi in armoniche sferiche di funzioni regolari a tratti, Tesi di Laurea, Università degli Studi di Milano (1998).
- [32] A.N. Varchenko, Number of lattice points in families of homethetic domains in Rn, Funktional An. 17 (1983), 1-6. Zbl0522.10031MR705041
- [33] G.N. Watson, "A treatise on the theory of Bessel functions", Cambridge University Press, 1944. Zbl0063.08184MR10746
- [34] H. Weyl, Die Gibbsche Erscheinung in der Theorie der Kugelfunktionen, Rendiconti Circ. Mat. Palermo29 (1910), 308-323. Zbl41.0528.01JFM41.0528.01
- [35] H. Weyl, Über die Gibbsche Erscheinung und verwandte Konvergenzphänomene, Rendiconti Circ. Mat. Palermo30 (1910), 377-407. JFM41.0528.02
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