# 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 (1996)

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

## Access Full Article

top## How to cite

topShlapunov, 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

top- [AnNa] A. Andreotti - M. Nacinovich, On analytic and C∞ Poincaré Lemma, Mathematical Analysis and Applications. Advances in Math. suppl. studies, 7A (81), pp. 41-93 Zbl0471.58021
- [Bj] J.E. Bjork, Rings of Differential Operators, North-Holland, New York (1979). Zbl0499.13009MR549189
- [Hö] L. Hörmander, L2-estimates and existence theorems for the ∂ operator, Acta Math., 113, 1-2 (1965), pp. 89-152. Zbl0158.11002
- [Ke] N. Kerzman, Hölder and Lp-estimates for solutions of ∂0 = f, Comm. Pure Appl. Math., 24, 3 (1971), pp. 89-152.
- [Ky] A.M. Kytmanov, The Bochner-Martinelli Integral, and its Applications, Nauka, Siberian branch Novosibirsk (1992); English transl. in Birkhäuser, Berlin (1995). Zbl0756.32001MR1409816
- [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
- [ReSz] S. Rempel - B.-W. Shulze, Index Theory of Elliptic Boundary Problems, Akademie-Verlag, Berlin (1982). Zbl0504.35002MR690065
- [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
- [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
- [Sh1] A.A. Shlapunov, On the Cauchy problem for Laplace's operator, Siberian Math. Journ., 33 (1992-93), pp. 205-215. Zbl0773.31007MR1178472
- [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
- [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
- [Ta] N.N. Tarkhanov, Laurent Series for Solutions of Elliptic Systems, Nauka, Novosibirsk (1991) (in Russian). Zbl0743.35021MR1226897
- [Tr] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, VEB Wiss. Verlag, Berlin (1978). Zbl0387.46033MR500580
- [VI] V.S. Vladimirov, Equations of Mathematical Physics, Nauka, Moscow (1988); English transl. in M. Dekker, New York (1971). Zbl0652.35002

## NotesEmbed ?

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