Local uniform convergence of the Riesz means of Laplace and Dirac expansions

Miklòs Horváth

Annales de la Faculté des sciences de Toulouse : Mathématiques (1997)

  • Volume: 6, Issue: 4, page 653-696
  • ISSN: 0240-2963

How to cite

top

Horváth, Miklòs. "Local uniform convergence of the Riesz means of Laplace and Dirac expansions." Annales de la Faculté des sciences de Toulouse : Mathématiques 6.4 (1997): 653-696. <http://eudml.org/doc/73438>.

@article{Horváth1997,
author = {Horváth, Miklòs},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {nonself-adjoint extensions; localization principle},
language = {eng},
number = {4},
pages = {653-696},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Local uniform convergence of the Riesz means of Laplace and Dirac expansions},
url = {http://eudml.org/doc/73438},
volume = {6},
year = {1997},
}

TY - JOUR
AU - Horváth, Miklòs
TI - Local uniform convergence of the Riesz means of Laplace and Dirac expansions
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1997
PB - UNIVERSITE PAUL SABATIER
VL - 6
IS - 4
SP - 653
EP - 696
LA - eng
KW - nonself-adjoint extensions; localization principle
UR - http://eudml.org/doc/73438
ER -

References

top
  1. [1] Alimov ( S.A.) .— On spectral decompositions of functions in Hαp, Math. USSR Sbornik30, n° 1 (1976), pp. 1-16. Zbl0381.46029
  2. [2] Alimov ( S.A.) and Joó ( I.) .— On the Riesz summability of eigenfunction expansions, Acta Sci. Math. Szeged45 (1983), pp. 5-18. Zbl0554.35030MR708767
  3. [3] Bateman ( H.) and Erdélyi ( A.) .— Higher transcendental functions, McGraw-Hill, New York, 1-2 (1953). Zbl0051.30303MR58756
  4. [4] Bergh ( J.) and Löfström ( J.) .— Interpolation spaces, An introduction, Springer, Berlin (1976). Zbl0344.46071MR482275
  5. [5] Evans ( W.D.) . - Eigenfunction expansions associated with the Dirac relativistic equations I-II, Quart. J. Math. Oxford17 (1966), pp. 211-233; 18 (1967), pp. 239-262. Zbl0144.23601MR217457
  6. [6] Horváth ( M.) .— Sur le développement spectral de l'opérateur de Schrödinger, Comptes Rendus Acad. Sci.Paris, Série I, 311 (1990), pp. 499-502. Zbl0711.47027MR1078109
  7. [7] Horváth ( M.) . - Exact norm estimates for the singular Schrödinger operator, Acta Math. Hung.60 (1992), pp. 177-195. Zbl0815.47061MR1177254
  8. [8] Horváth ( M.) .— Uniform estimations of the Green function for the singular Schrödinger operator, Acta Math. Hung.61 (1993), pp. 327-342. Zbl0820.35102MR1214640
  9. [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. Zbl0821.35105MR1261483
  10. [10] Horváth ( M.), Joó ( I.) and Komornik ( V.) .- An equiconvergence theorem, Annales Univ. Sci. Budapest, Sectio Math.31 (1988), pp. 19-26. Zbl0684.34031MR1003626
  11. [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. Zbl0224.35014MR284868
  12. [12] Joó ( I.) .- On the summability of eigenfunction expansions I, Acta Math. Hung.43, n° 1-2 (1984), pp. 73-83. Zbl0539.35058MR731967
  13. [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. Zbl0657.35093MR856998
  14. [14] Joó ( I.) .— On the uniform Riesz summability of eigenfunction expansions I, Annales Univ. Sci. Budapest, Sectio Math.31 (1988), pp. 191-211. Zbl0694.35124MR1003646
  15. [15] Joó ( I.) .— Exact estimate for the spectral function of the singular Schrödinger operator, Periodica Math. Hung.18, n° 3 (1987), pp. 203-211. Zbl0633.35056MR902523
  16. [16] Joó ( I.) .- On the divergence of eigenfunction expansions, Annales Univ. Sci. Budapest, Sectio Math.32 (1989), pp. 3-36. Zbl0734.42018MR1094655
  17. [17] Joó ( I.) .— On the convergence of eigenfunction expansions, Acta Math. Hung.60 (1992), pp. 125-156. Zbl0807.35103MR1177252
  18. [18] Joó ( I.) and Komornik ( V.) .— On the equiconvergence of expansions by Riesz bases formed by eigenfunctions of the Schrödinger operator, Acta Sci. Math. Szeged46 (1983), pp. 357-375. Zbl0537.34019MR739055
  19. [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. Zbl0562.42023MR762724
  20. [20] Nikiforov ( A.) and Ouvarov ( V.) .— Fonctions spéciales de la physique mathématique, Édition Mir, Moscou (1983). 
  21. [21] Nikolskii ( S.M.) .— Approximation of functions of several variables and imbedding theorems, Nauka, Moscow (1977), in Russian. Zbl0496.46020MR506247
  22. [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. Zbl0466.46018MR643384
  23. [23] Titchmarsh ( E.C.) . — Eigenfunction expansions associated with second order differential equations I-II, Clarendon Press, Oxford1946, 1958. Zbl0061.13505
  24. [24] Triebel ( H.) .- Interpolation theory. Functions spaces. Differential operators, V.E.B. Verlag, Berlin (1978). Zbl0387.46033
  25. [25] Watson ( G.N.) .- A treatise on the theory of Bessel functions, Cambridge Univ. Press (1952). JFM50.0264.01
  26. [26] Young ( R.M.) .- An introduction to nonharmonic Fourier series, Academic Press, New York (1980). Zbl0493.42001MR591684
  27. [27] Zygmund ( A.) .- Trigonometric Series, Cambridge Univ. Press (1959). Zbl0085.05601

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.