Spectral decomposition of Green’s integrals and existence of W s , 2 -solutions of matrix factorizations of the Laplace operator in a ball

A. Shlapunov

Rendiconti del Seminario Matematico della Università di Padova (1996)

  • Volume: 96, page 237-256
  • ISSN: 0041-8994

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Shlapunov, A.. "Spectral decomposition of Green’s integrals and existence of $W^{s,2}$-solutions of matrix factorizations of the Laplace operator in a ball." Rendiconti del Seminario Matematico della Università di Padova 96 (1996): 237-256. <http://eudml.org/doc/108412>.

@article{Shlapunov1996,
author = {Shlapunov, A.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {fundamental solution; solvability; harmonic functions; Green's integral},
language = {eng},
pages = {237-256},
publisher = {Seminario Matematico of the University of Padua},
title = {Spectral decomposition of Green’s integrals and existence of $W^\{s,2\}$-solutions of matrix factorizations of the Laplace operator in a ball},
url = {http://eudml.org/doc/108412},
volume = {96},
year = {1996},
}

TY - JOUR
AU - Shlapunov, A.
TI - Spectral decomposition of Green’s integrals and existence of $W^{s,2}$-solutions of matrix factorizations of the Laplace operator in a ball
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1996
PB - Seminario Matematico of the University of Padua
VL - 96
SP - 237
EP - 256
LA - eng
KW - fundamental solution; solvability; harmonic functions; Green's integral
UR - http://eudml.org/doc/108412
ER -

References

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  2. [Bj] J.E. Bjork, Rings of Differential Operators, North-Holland, New York (1979). Zbl0499.13009MR549189
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  5. [Ky] A.M. Kytmanov, The Bochner-Martinelli Integral, and its Applications, Nauka, Siberian branch Novosibirsk (1992); English transl. in Birkhäuser, Berlin (1995). Zbl0756.32001MR1409816
  6. [NaSh] M. Nacinovich - A.A. Shlapunov, On iterations of the Green integrals and their applications to elliptic differential complexes, Prepr. Sezione di Analisi e Probabilità, Dipartimento di Matematica, Universita di Pisa, 2.170.805 (1994); Mathematiche Nachrichten (1995), to appear. Zbl0871.35066MR1397675
  7. [ReSz] S. Rempel - B.-W. Shulze, Index Theory of Elliptic Boundary Problems, Akademie-Verlag, Berlin (1982). Zbl0504.35002MR690065
  8. [Rom1] A.V. Romanov, Spectral analysis of Martinelli-Bochner integral for ball in Cn, and its application, Functional. Anal. i Prilozhen., 12, 3 (1978); English transl. in Funct. Anal. Appl, 12, 3 (1978). Zbl0401.47023MR509397
  9. [Rom1] A.V. Romanov, Convergence of iterations of Bochner-Martinelli operator, and the Cauchy-Riemann system, Dokl. Akad. Nauk SSSR, 2424 (1978), pp. 780-783; English transl. in Soviet Math. Dokl., 19, 5 (1978). Zbl0434.35066MR509378
  10. [Sh1] A.A. Shlapunov, On the Cauchy problem for Laplace's operator, Siberian Math. Journ., 33 (1992-93), pp. 205-215. Zbl0773.31007MR1178472
  11. [Sh2] A.A. Shlapunov, On iterations of Green type integrals for matrix factorizations of the Laplace operator, Rend. Mat. Ace. Lincei, 9, 2 (1994), pp. 103-116. Zbl0873.32016MR1292566
  12. [ShTa] A.A. Shlapunov - N.N. Tarkhanov, Bases with double orthogonality in the Cauchy problem for systems with injective symbol, The Proceedings of the London Math. Soc. (3), 71 (1995). Zbl0828.35040MR1327932
  13. [Ta] N.N. Tarkhanov, Laurent Series for Solutions of Elliptic Systems, Nauka, Novosibirsk (1991) (in Russian). Zbl0743.35021MR1226897
  14. [Tr] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, VEB Wiss. Verlag, Berlin (1978). Zbl0387.46033MR500580
  15. [VI] V.S. Vladimirov, Equations of Mathematical Physics, Nauka, Moscow (1988); English transl. in M. Dekker, New York (1971). Zbl0652.35002

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