Weitere Formate
Autorenfreundlich Bücher kaufen?!
Beschreibung
0.1 The partial differential equation (1) (Au)(x) = L aa(x)(Dau)(x) = f(x) m lal9 is called elliptic on a set G, provided that the principal symbol a2m(X,¿) = L aa(x)¿a lal=2m of the operator A is invertible on G X (~n \ 0); A is called elliptic on G, too. This definition works for systems of equations, for classical pseudo differential operators ("pdo), and for operators on a manifold n. Let us recall some facts concerning elliptic operators. 1 If n is closed, then for any s E ~ , is Fredholm and the following a priori estimate holds (2) 1 2 Introduction If m > 0 and A : C=(O; C') -+ L (0; C') is formally self - adjoint 2 with respect to a smooth positive density, then the closure Ao of A is a self - adjoint operator with discrete spectrum and for the distribu tion functions of the positive and negative eigenvalues (counted with multiplicity) of Ao one has the following Weyl formula: as t -+ 00, (3) n 2m = t / II N±(1,a2m(x,e))dxde T·O\O (on the right hand side, N±(t,a2m(x,e))are the distribution functions of the matrix a2m(X,e) : C' -+ CU).
Details
| Verlag | Springer Netherland |
| Ersterscheinung | 15. Dezember 2010 |
| Maße | 29.7 cm x 21 cm |
| Gewicht | 674 Gramm |
| Format | Softcover |
| ISBN-13 | 9789048142828 |
| Auflage | Softcover reprint of hardcover 1st edition 1993 |
| Seiten | 436 |
Schlagwörter
Herstellerinformationen
Bekannt durch
