Geodesic
On Bojarski’s index formula for nonsmooth interfaces
Mitrea, Marius1
1Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211
Electronic research announcements of the American Mathematical Society, Tome 05 (1999), pp. 40-46

Voir la notice de l'article provenant de la source American Mathematical Society

DOI

Let $D$ be a Dirac type operator on a compact manifold ${\mathcal {M}}$ and let $\Sigma$ be a Lipschitz submanifold of codimension one partitioning ${\mathcal {M}}$ into two Lipschitz domains $\Omega _{\pm }$. Also, let ${\mathcal {H}}^{p}_{\pm }(\Sigma ,D)$ be the traces on $\Sigma$ of the ($L^{p}$-style) Hardy spaces associated with $D$ in $\Omega _{\pm }$. Then $({\mathcal {H}}^{p}_{-}(\Sigma ,D),{\mathcal {H}}^{p}_{+}(\Sigma ,D))$ is a Fredholm pair of subspaces for $L^{p}(\Sigma )$ (in Kato’s sense) whose index is the same as the index of the Dirac operator $D$ considered on the whole manifold ${\mathcal {M}}$.
DOI : 10.1090/S1079-6762-99-00060-8

Mitrea, Marius  1

1 Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211 
Mitrea, Marius. On Bojarski’s index formula for nonsmooth interfaces. Electronic research announcements of the American Mathematical Society, Tome 05 (1999), pp. 40-46. doi: 10.1090/S1079-6762-99-00060-8
@article{10_1090_S1079_6762_99_00060_8,
     author = {Mitrea, Marius},
     title = {On {Bojarski{\textquoteright}s} index formula for nonsmooth interfaces},
     journal = {Electronic research announcements of the American Mathematical Society},
     pages = {40--46},
     year = {1999},
     volume = {05},
     doi = {10.1090/S1079-6762-99-00060-8},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-99-00060-8/}
}
TY  - JOUR
AU  - Mitrea, Marius
TI  - On Bojarski’s index formula for nonsmooth interfaces
JO  - Electronic research announcements of the American Mathematical Society
PY  - 1999
SP  - 40
EP  - 46
VL  - 05
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-99-00060-8/
DO  - 10.1090/S1079-6762-99-00060-8
ID  - 10_1090_S1079_6762_99_00060_8
ER  - 
%0 Journal Article
%A Mitrea, Marius
%T On Bojarski’s index formula for nonsmooth interfaces
%J Electronic research announcements of the American Mathematical Society
%D 1999
%P 40-46
%V 05
%U http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-99-00060-8/
%R 10.1090/S1079-6762-99-00060-8
%F 10_1090_S1079_6762_99_00060_8

[1] Maclane, Saunders, Schilling, O. F. G. Infinite number fields with Noether ideal theories Amer. J. Math. 1939 771 782

[2] Boyarski, B. An abstract problem of linear conjugation and Fredholm pairs of subspaces 1979 45 60

[3] Booss, Bernhelm, Wojciechowski, Krzysztof Desuspension of splitting elliptic symbols. II Ann. Global Anal. Geom. 1986 349 400

[4] Booß-Bavnbek, Bernhelm, Wojciechowski, Krzysztof P. Elliptic boundary problems for Dirac operators 1993

[5] Coifman, R. R., Mcintosh, A., Meyer, Y. L’intégrale de Cauchy définit un opérateur borné sur 𝐿² pour les courbes lipschitziennes Ann. of Math. (2) 1982 361 387

[6] Maclane, Saunders, Schilling, O. F. G. Infinite number fields with Noether ideal theories Amer. J. Math. 1939 771 782

[7] David, Guy Opérateurs intégraux singuliers sur certaines courbes du plan complexe Ann. Sci. École Norm. Sup. (4) 1984 157 189

[8] Gilbert, John E., Murray, Margaret A. M. Clifford algebras and Dirac operators in harmonic analysis 1991

[9] Kato, Tosio Perturbation theory for linear operators 1976

[10] Kenig, Carlos E. Weighted 𝐻^{𝑝} spaces on Lipschitz domains Amer. J. Math. 1980 129 163

[11] Li, Chun, Mcintosh, Alan, Semmes, Stephen Convolution singular integrals on Lipschitz surfaces J. Amer. Math. Soc. 1992 455 481

[12] Meyer, Yves, Coifman, R. R. Ondelettes et opérateurs. III 1991

[13] Mitrea, Marius Clifford wavelets, singular integrals, and Hardy spaces 1994

[14] Perlis, Sam Maximal orders in rational cyclic algebras of composite degree Trans. Amer. Math. Soc. 1939 82 96

[15] Nicolaescu, Liviu I. The Maslov index, the spectral flow, and decompositions of manifolds Duke Math. J. 1995 485 533

[16] Taylor, Michael E. Pseudodifferential operators and nonlinear PDE 1991 213

Cité par Sources :