The Analysis of Linear Partial Differential Operators II: Differential Operators with Constant CoefficientsSpringer Berlin Heidelberg, 30 janv. 1990 - 392 pages This volume is an expanded version of Chapters III, IV, V and VII of my 1963 book "Linear partial differential operators". In addition there is an entirely new chapter on convolution equations, one on scattering theory, and one on methods from the theory of analytic functions of several complex variables. The latter is somewhat limited in scope though since it seems superfluous to duplicate the monographs by Eh renpreis and by Palamodov on this subject. The reader is assumed to be familiar with distribution theory as presented in Volume I. Most topics discussed here have in fact been encountered in Volume I in special cases, which should provide the necessary motivation and background for a more systematic and pre cise exposition. The main technical tool in this volume is the Fourier- Laplace transformation. More powerful methods for the study of operators with variable coefficients will be developed in Volume III. However, the constant coefficient theory has given the guidehnes for all that work. Although the field is no longer very active - perhaps because of its advanced state of development - and although it is pos sible to pass directly from Volume I to Volume III, the material pre sented here should not be neglected by the serious student who wants to gain a balanced perspective of the theory of linear partial differen tial equations. |
Autres éditions - Tout afficher
The Analysis of Linear Partial Differential Operators: Differential ... Lars Hörmander Affichage d'extraits - 1983 |
The Analysis of Linear Partial Differential Operators II: Differential ... Lars Hörmander Affichage d'extraits - 1990 |
Expressions et termes fréquents
analytic function apply assume boundary bounded C₁ Cauchy data Cauchy problem choose compact set compact subset compact support completes the proof condition cone conic neighborhood constant coefficients constant strength continuous converges convex set Corollary defined Definition denote differential operators distribution elliptic equal equivalent estimate existence finite follows from Theorem Fourier transform Fréchet space fundamental solution gives Hence homogeneous Hörmander hyperbolic with respect hypoelliptic hypothesis implies inequality integral K₂ Lemma linear Math mixed problem neighborhood norm obtain open set P-convex for supports partition of unity plurisubharmonic functions polynomial proof is complete proof of Theorem Proposition proves the theorem pseudo-differential operators replaced right-hand side satisfies Section semi-algebraic sequence shows sing supp singular supports subharmonic function supporting function suppu topology u₁ valid vanishes veCo X₁ zeros