Geodesic
On spectral projection for the complex Neumann problem
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 4, pp. 439-450 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We show that the $L^2$-spectral kernel function of the $\bar\partial$-Neumann problem on a non-compact strongly pseudoconvex manifold is smooth up to the boundary.
Keywords: $\bar\partial$-Neumann problem, strongly pseudoconvex domains, spectral kernel function. 
@article{JSFU_2012_5_4_a0,
     author = {Ammar Alsaedy and Nikolai Tarkhanov},
     title = {On spectral projection for the complex {Neumann} problem},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {439--450},
     year = {2012},
     volume = {5},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2012_5_4_a0/}
}
TY  - JOUR
AU  - Ammar Alsaedy
AU  - Nikolai Tarkhanov
TI  - On spectral projection for the complex Neumann problem
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2012
SP  - 439
EP  - 450
VL  - 5
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/JSFU_2012_5_4_a0/
LA  - en
ID  - JSFU_2012_5_4_a0
ER  - 
%0 Journal Article
%A Ammar Alsaedy
%A Nikolai Tarkhanov
%T On spectral projection for the complex Neumann problem
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2012
%P 439-450
%V 5
%N 4
%U http://geodesic.mathdoc.fr/item/JSFU_2012_5_4_a0/
%G en
%F JSFU_2012_5_4_a0
Ammar Alsaedy; Nikolai Tarkhanov. On spectral projection for the complex Neumann problem. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 4, pp. 439-450. http://geodesic.mathdoc.fr/item/JSFU_2012_5_4_a0/

[1] C. B. Morrey, Multiple Integrals in the Calculus of Variations, Springer-Verlag, Berlin et al., 1966 | MR | Zbl

[2] J. J. Kohn, “Harmonic integrals on strongly pseudoconvex manifolds. I”, Ann. Math., 78:1 (1963), 112–148 ; “II”, Ann. Math., 79:3 (1964), 450–472 | DOI | MR | Zbl | DOI | MR | Zbl

[3] H. R. Boas, E. J. Straube, “Global regularity of the $\bar\partial$-Neumann problem: A survey of the $L^2$-Sobolev theory”, Several Complex Variables, 37 (1999), 79–111 | MR | Zbl

[4] J. J. Kohn, L. Nirenberg, “Non-coercive boundary value problems”, Comm. Pure Appl. Math., 18 (1965), 443–492 | DOI | MR | Zbl

[5] I. Lieb, J. Michel, The Cauchy-Riemann Complex, Vieweg, Braunschweig/Wiesbaden, 2002 | MR | Zbl

[6] R. Beals, N. K. Stanton, “Estimates on kernels for the $\bar\partial$-equation and the $\bar\partial$-Neumann problem”, Math. Ann., 289 (1991), 73–83 | DOI | MR | Zbl

[7] A. Nagel, E. M. Stein, Lectures on Pseudo-Differential Operators: Regularity Theorems and Applications to Non-Elliptic Problems, Princeton University Press, Princeton, New Jersey, 1979 | MR | Zbl

[8] M. Englis, “Pseudolocal estimates for $\bar\partial$ on general pseudoconvex domains”, Indiana Univ. Math. J., 50 (2001), 1593–1607 | DOI | MR | Zbl

[9] G. Métivier, “Spectral asymptotics for the $\bar\partial$-Neumann problem”, Duke Math. J., 48 (1981), 779–806 | DOI | MR | Zbl

[10] R. Beals, N. K. Stanton, “The heat equation for the $\bar\partial$-Neumann problem. I”, Comm. Part. Diff. Eq., 12 (1987), 351–413 ; “II”, Canad. J. Math., 40 (1988), 502–512 | DOI | MR | Zbl | DOI | MR | Zbl

[11] D. M. McAvity, H. Osborn, “Asymptotic expansion of the heat kernel for generalized boundary conditions”, Classical Quantum Grav., 8 (1991), 1445–1454 | DOI | MR | Zbl

[12] N. Tarkhanov, Complexes of Differential Operators, Kluwer Academic Publishers, Dordrecht, NL, 1995 | MR | Zbl

[13] F. Riesz, B. Sz.-Nagy, Lecons d'Analyse {F}onctionnelle, Acad. des Sci. de Hongrie, Budapest, 1952 | MR

[14] Ya. A. Roitberg, Elliptic boundary value problems in the spaces of distributions, Kluwer Academic Publishers, Dordrecht, NL, 1996 | MR | Zbl

[15] N. Kerzman, “The Bergman kernel function. Differentiability at the boundary”, Math. Ann., 195 (1972), 149–158 | DOI | MR