no. 3
Decay of Fourier transforms and summability of eigenfunction expansions
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 29 (2000) no. 3, pp. 611-638 
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     author = {Brandolini, Luca and Colzani, Leonardo},
     title = {Decay of {Fourier} transforms and summability of eigenfunction expansions},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {611--638},
     year = {2000},
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     number = {3},
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     url = {https://www.numdam.org/item/ASNSP_2000_4_29_3_611_0/}
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Brandolini, Luca; Colzani, Leonardo. Decay of Fourier transforms and summability of eigenfunction expansions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 29 (2000) no. 3, pp. 611-638. https://www.numdam.org/item/ASNSP_2000_4_29_3_611_0/

[1] S.A. Alimov - V.A. Il'In - E.M. Nikishin, Convergence problems of multiple trigonometric series and spectral decompositions, I, II, Russian Math. Surveys 31 (1976), 29-86, 32 (1977), 115-139. | Zbl

[2] P. Bérard, On the wave equation on a manifold without conjugate points, Math. Z. 155 (1977), 249-276. | Zbl | MR

[3] P. Bérard, Riesz means on Riemannian manifolds, Amer. Math. Soc. Proc. Symp. Pure Math. XXXVI (1980), 1-12. | Zbl | MR

[4] S. Bochner, Summation of multiple Fourier series by spherical means, Trans. Amer. Math. Soc. 40 (1936), 175-207. | Zbl | MR | JFM

[5] L. Brandolini - L. Colzani, Localization and convergence of eigenfunction expansions, J. Fourier Anal. Appl. 5 (1999), 431-447. | Zbl | MR

[6] L. Brandolini - L. Colzani - G. Travaglini, Average decay of Fourier transforms and integer points in polyhedra, Ark. Mat. 35 (1997), 253-275. | Zbl | MR

[7] L. Colzani - M. Vignati, The Gibbs phenomenon for multiple Fourier integrals, J. Approx. Th. 80 (1995), 119-131. | Zbl | MR

[8] L. De Michele - D. Roux, Approximate units and Gibbs phenomenon, Boll. Un. Mat. Ital. A (7) (1997), 739-746. | Zbl | MR

[9] L. De Michele - D. Roux, The Gibbs phenomenon for L1 loc kernels, J. Approx. Th. 100 (1999), 144-156. | Zbl | MR

[10] L. De Michele - D. Roux, The Gibbs phenomenon for multiple Fourier integrals and series: restriction theorems, Atti Sem. Mat. Fis. Univ. Modena 46 (1998), 351-360. | Zbl | MR

[11] G.H. Hardy, On the expression of a number as a sum of two squares, Quart. J. Math. 46 (1915), 263-283. | JFM

[12] E. Hlawka, Uber Integrale auf convexen Korpen, I & II, Monats. Math. 54 (1950), 1-36, 81-99. | Zbl | MR | EuDML

[13] C. Herz, Fourier transform related to convex sets, Ann. of Math. 75 (1962), 81-92. | Zbl | MR

[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 University 1966, pp. 155-202. | MR

[15] L. Hörmander, The spectral function of an elliptic operator, Acta Math. 121 (1968), 193-218. | Zbl | MR

[16] L. Hörmander, "The analysis of linear partial differential operators", I, II, III, IV, Springer Verlag, 1985-1985. | MR | Zbl

[17] J.P. Kahane, Le phénomène de Pinsky et la géométrie des surfaces, C. R. Acad. Sci. Paris 321 (1995), 1027-1029. | Zbl | MR

[18] D.G. Kendall, On the number of lattice points inside a random oval, Quart. J. Math. Oxford 19 (1948), 1-26. | Zbl | MR

[19] C. Meaney, On almost-everywhere convergent eigenfunction expansions of the Laplace-Beltrami operator, Math. Proc. Cambridge Philos. Soc. 92 (1982), 129-131. | Zbl | MR

[20] M.A. Pinsky, Pointwise Fourier inversion and related eigenfunction expansions, Comm. Pure Appl. Math. 47 (1994), 653-681. | Zbl | MR

[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). | Zbl | MR

[22] M.A. Pinsky - M. Taylor, Pointwise Fourier inversion: a wave equation approach, J. Fourier Anal. Appl. 3 (1997), 647-703. | Zbl | MR | EuDML

[23] A.N. Podkorytov, The asymptotic of Fourier transform of a convex curve, Vestnik Leningr. Univ. Mat. 24 (1991), 57-65. | Zbl | MR

[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. | Zbl | MR

[25] C.D. Sogge, On the convergence of Riesz means on compact manifolds, Ann. of Math. 126 (1987), 439-447. | Zbl | MR

[26] E.M. Stein - G. Weiss, "Introduction to Fourier analysis on Euclidean spaces", Princeton University Press, 1971. | Zbl | MR

[27] M.E. Taylor, Pointwise Fourier inversion on tori and other compact manifolds, J. Fourier Anal. Appl. 5 (1999), 449-463. | Zbl | MR | EuDML

[28] M.E. Taylor, Pointwise Fourier inversion - an addendum, Proc. Amer. Math. Soc., to appear. | Zbl | MR

[29] M.E. Taylor, The Dirichlet-Jordan test and multidimensional extensions, Proc. Amer. Math. Soc., to appear. | Zbl | MR

[30] M.E. Taylor, Eigenfunction expansions and the Pinsky phenomenon on compact manifolds, preprint. | MR | Zbl

[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. | Zbl | MR

[33] G.N. Watson, "A treatise on the theory of Bessel functions", Cambridge University Press, 1944. | Zbl | MR

[34] H. Weyl, Die Gibbsche Erscheinung in der Theorie der Kugelfunktionen, Rendiconti Circ. Mat. Palermo 29 (1910), 308-323. | JFM

[35] H. Weyl, Über die Gibbsche Erscheinung und verwandte Konvergenzphänomene, Rendiconti Circ. Mat. Palermo 30 (1910), 377-407. | JFM