Local uniform convergence of the Riesz means of Laplace and Dirac expansions
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 6 (1997) no. 4, pp. 653-696. 
@article{AFST_1997_6_6_4_653_0,
     author = {Horv\'ath, Mikl\`os},
     title = {Local uniform convergence of the {Riesz} means of {Laplace} and {Dirac} expansions},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {653--696},
     publisher = {Universit\'e Paul Sabatier. Facult\'e des sciences},
     address = {Toulouse},
     volume = {Ser. 6, 6},
     number = {4},
     year = {1997},
     mrnumber = {1624310},
     zbl = {0914.35090},
     language = {en},
     url = {http://archive.numdam.org/item/AFST_1997_6_6_4_653_0/}
}
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Horváth, Miklòs. Local uniform convergence of the Riesz means of Laplace and Dirac expansions. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 6 (1997) no. 4, pp. 653-696. http://archive.numdam.org/item/AFST_1997_6_6_4_653_0/

[1] Alimov (S.A.) .- On spectral decompositions of functions in Hαp, Math. USSR Sbornik 30, n° 1 (1976), pp. 1-16. | Zbl

[2] Alimov (S.A.) and Joó (I.) .- On the Riesz summability of eigenfunction expansions, Acta Sci. Math. Szeged 45 (1983), pp. 5-18. | MR | Zbl

[3] Bateman (H.) and Erdélyi (A.) .- Higher transcendental functions, McGraw-Hill, New York, 1-2 (1953). | MR | Zbl

[4] Bergh (J.) and Löfström (J.) .- Interpolation spaces, An introduction, Springer, Berlin (1976). | MR | Zbl

[5] Evans (W.D.) . - Eigenfunction expansions associated with the Dirac relativistic equations I-II, Quart. J. Math. Oxford 17 (1966), pp. 211-233; 18 (1967), pp. 239-262. | MR | Zbl

[6] Horváth (M.) .- Sur le développement spectral de l'opérateur de Schrödinger, Comptes Rendus Acad. Sci. Paris, Série I, 311 (1990), pp. 499-502. | MR | Zbl

[7] Horváth (M.) . - Exact norm estimates for the singular Schrödinger operator, Acta Math. Hung. 60 (1992), pp. 177-195. | MR | Zbl

[8] Horváth (M.) .- Uniform estimations of the Green function for the singular Schrödinger operator, Acta Math. Hung. 61 (1993), pp. 327-342. | MR | Zbl

[9] Horváth (M.) . - Local uniform convergence of the eigenfunction expansion associated with the Laplace operator I-II, Acta Math. Hung. 64 (1994), pp. 1-25, 101-138. | MR | Zbl

[10] Horváth (M.), Joó (I.) and Komornik (V.) .- An equiconvergence theorem, Annales Univ. Sci. Budapest, Sectio Math. 31 (1988), pp. 19-26. | MR | Zbl

[11] Il'In (V.A.) and Alimov (S.A.) .- Convergence conditions for the spectral expansions associated with selfadjoint extensions of elliptic operators I-II, Differencialnie Uravnenija (in Russian) 7, n° 4 (1971), pp. 670-710; 7, n° 5 (1971), pp. 851-882. | MR | Zbl

[12] Joó (I.) .- On the summability of eigenfunction expansions I, Acta Math. Hung. 43, n° 1-2 (1984), pp. 73-83. | MR | Zbl

[13] Joó (I.) .- On the summability of eigenfunction expansions II, III, Annales Univ. Sci. Budapest, Sectio Math. 27 (1985), pp. 167-184; 28 (1986), pp. 253-262. | MR | Zbl

[14] Joó (I.) .- On the uniform Riesz summability of eigenfunction expansions I, Annales Univ. Sci. Budapest, Sectio Math. 31 (1988), pp. 191-211. | MR | Zbl

[15] Joó (I.) .- Exact estimate for the spectral function of the singular Schrödinger operator, Periodica Math. Hung. 18, n° 3 (1987), pp. 203-211. | MR | Zbl

[16] Joó (I.) .- On the divergence of eigenfunction expansions, Annales Univ. Sci. Budapest, Sectio Math. 32 (1989), pp. 3-36. | MR | Zbl

[17] Joó (I.) .- On the convergence of eigenfunction expansions, Acta Math. Hung. 60 (1992), pp. 125-156. | MR | Zbl

[18] Joó (I.) and Komornik (V.) .- On the equiconvergence of expansions by Riesz bases formed by eigenfunctions of the Schrödinger operator, Acta Sci. Math. Szeged 46 (1983), pp. 357-375. | MR | Zbl

[19] Komornik (V.) .- Sur l'équiconvergence des séries orthogonales et biorthogonales correspondant aux fonctions propres des opérateurs différentiels linéaires, Comptes Rendus Acad. Sci. Paris, Série I, 299 (1984), pp. 217-219. | MR | Zbl

[20] Nikiforov (A.) and Ouvarov (V.) .- Fonctions spéciales de la physique mathématique, Édition Mir, Moscou (1983).

[21] Nikolskii (S.M.) .- Approximation of functions of several variables and imbedding theorems, Nauka, Moscow (1977), in Russian. | MR | Zbl

[22] Nikolskii (N.K.), Pavlov (B.S.) and Hruscov (S.V.) .- Unconditional bases of exponentials and of reproducing kernels, Lecture Notes in Math., Springer, Berlin, 864 (1981), pp. 214-335. | MR | Zbl

[23] Titchmarsh (E.C.) . - Eigenfunction expansions associated with second order differential equations I-II, Clarendon Press, Oxford 1946, 1958. | Zbl

[24] Triebel (H.) .- Interpolation theory. Functions spaces. Differential operators, V.E.B. Verlag, Berlin (1978). | Zbl

[25] Watson (G.N.) .- A treatise on the theory of Bessel functions, Cambridge Univ. Press (1952). | JFM

[26] Young (R.M.) .- An introduction to nonharmonic Fourier series, Academic Press, New York (1980). | MR | Zbl

[27] Zygmund (A.) .- Trigonometric Series, Cambridge Univ. Press (1959). | Zbl