On iterations of Green type integrals for matrix factorizations of the Laplace operator

Alexandre A. Shlapunov

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1994)

  • Volume: 5, Issue: 2, page 103-116
  • ISSN: 1120-6330

Abstract

top
Convergence of special Green integrals for matrix factorization of the Laplace operator in R n is proved. Explicit formulae for solutions of ∂ ¯ -equation in strictly pseudo-convex domains in C n are obtained.

How to cite

top

Shlapunov, Alexandre A.. "On iterations of Green type integrals for matrix factorizations of the Laplace operator." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 5.2 (1994): 103-116. <http://eudml.org/doc/244096>.

@article{Shlapunov1994,
abstract = {Convergence of special Green integrals for matrix factorization of the Laplace operator in \( \mathbb\{R\}^\{n\} \) is proved. Explicit formulae for solutions of \( \bar\{\partial\} \)-equation in strictly pseudo-convex domains in \( C^\{n\} \) are obtained.},
author = {Shlapunov, Alexandre A.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Green integral; Differential operator with injective symbol; Dolbeault complex; differential operator with injective symbol; Green integrals; matrix factorization; Laplace operator; -equation; strictly pseudo-convex domains},
language = {eng},
month = {6},
number = {2},
pages = {103-116},
publisher = {Accademia Nazionale dei Lincei},
title = {On iterations of Green type integrals for matrix factorizations of the Laplace operator},
url = {http://eudml.org/doc/244096},
volume = {5},
year = {1994},
}

TY - JOUR
AU - Shlapunov, Alexandre A.
TI - On iterations of Green type integrals for matrix factorizations of the Laplace operator
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1994/6//
PB - Accademia Nazionale dei Lincei
VL - 5
IS - 2
SP - 103
EP - 116
AB - Convergence of special Green integrals for matrix factorization of the Laplace operator in \( \mathbb{R}^{n} \) is proved. Explicit formulae for solutions of \( \bar{\partial} \)-equation in strictly pseudo-convex domains in \( C^{n} \) are obtained.
LA - eng
KW - Green integral; Differential operator with injective symbol; Dolbeault complex; differential operator with injective symbol; Green integrals; matrix factorization; Laplace operator; -equation; strictly pseudo-convex domains
UR - http://eudml.org/doc/244096
ER -

References

top
  1. AIZENBERG, L. A. - YUZHAKOV, A. P., Integral Representations and Residues in Multidimensional Complex Analysis. American Mathematical Society, Providence1983. Zbl0537.32002MR735793
  2. BERNDTSSON, B. - ANDERSSON, M., Henkin-Ramires formulas with wight factors. Ann. Inst. Fourier, 142, 3, 1982, 91-110. Zbl0466.32001MR688022
  3. DAUTOV, SH. A. - HENKIN, G. M., Zeros of holomorphic functions of finite order and wight estimates. Matem. Sbornik, 107, 2, 1978, 163-174. Zbl0392.32001MR512005
  4. EGOROV, YU. V. - SHUBIN, M. A., Linear Partial Differential Equations: Foundations of Classical Theory. Springer, Berlin1992. Zbl0738.35001MR1141631
  5. FOLLAND, G. B. - KOHN, J. J., The Neumann Problem for the Cauchy-Riemann Complex. Princeton University Press, Princeton1972. Zbl0247.35093MR461588
  6. HARVEY, R. - POLKING, J., The ∂ ¯ -Neumann kernel in the ball in C n . Proc. Symp. Pure Math. J., 41, 1984, 117-136. Zbl0578.32030MR740876
  7. HENKIN, G. M., Method of integral representations in complex analysis. Results of Sciences and Technics, Modern Problems of Mathematics, Fundamental Trends, VINITI, 7, 1985, 23-125 (in Russian). Zbl0781.32007MR850491
  8. HENKIN, G. M. - LEITERER, J., Theory of Functions on Complex Manifolds. Akademie-Verlag, Berlin1984. Zbl0573.32001MR795028
  9. HÖRMANDER, L., An Introduction to Complex Analysis in Several Variables. Princeton1966. Zbl0138.06203
  10. KOHN, J. J., Subellipticity of the ∂ ¯ -Neumann problem on pseudo-convex domains: sufficient conditions. Acta Math., 142, 1-2, 1979, 79-122. Zbl0395.35069MR512213DOI10.1007/BF02395058
  11. KYTMANOV, A. M., The Bochner-Martinelli Integral, and its Applications. Nauka, Siberian branch, Novosibirsk1992 (in Russian). Zbl0756.32001
  12. LIONS, J. L. - MAGENES, E., Problèmes aux limites non homogènes et applications. I-III, Dunod, Paris1968. Zbl0165.10801
  13. REMPEL, S. - SHULZE, B. W., Index Theory of Elliptic boundary Problems. Akademie-Verlag, Berlin1982. Zbl0504.35002MR690065
  14. ROMANOV, A. V., Spectral analysis of Martinelli-Bochner integral for ball in C n and its application. Functional. Anal. i Prilozhen., 12, N3, 1978, 86-88; English transl, in Functional Anal. Appl., 12, N3, 1978, 232-234. Zbl0427.47035MR509397
  15. ROMANOV, A. V., Convergence of Iterations of Bochner-Martinelli Operator, and the Cauchy-Riemann System. Soviet Math. Dokl, 19, 5, 1978, 1211-1215. Zbl0434.35066
  16. SHIMAKURA, N., Partial Differential Operators of Elliptic Type. American Mathematical Society, Providence Rhode Island1992, 286 pp. Zbl0757.35015MR1168472
  17. SHLAPUNOV, A. A. - TARKHANOV, N. N., Bases with double orthogonality in the Cauchy problem for systems with injective symbol. Prepr. Inst, of Physics, Academy of Sciences, Siberian branch, Krasnoyarsk1990, 56M. Zbl0799.35167
  18. TARKHANOV, N. N., Parametrix Method in the Theory of Differential Complexes. Nauka, Novosibirsk1990. Zbl0758.58002MR1082557
  19. TARKHANOV, N. N., Laurent Series for Solutions of Elliptic Systems. Nauka, Novosibirsk1991. Zbl0743.35021MR1226897

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.