Bøger af Norbert Ortner

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

This monograph provides the theoretical foundations needed for the construction of fundamental solutions and fundamental matrices of (systems of) linear partial differential equations.

Homogeneous and, more generally, quasihomogeneous distributions represent an important subclass of L. Schwartz's distributions. In this book, the meromorphic dependence of these distributions on the order of homogeneity and on further parameters is studied. The analytic continuation, the residues and the finite parts of these distribution-valued functions are investigated in some detail.This research was initiated by Marcel Riesz in his seminal article in Acta Mathematica in 1949. It leads to the so-called elliptic and hyperbolic M. Riesz kernels referring to the Laplace and the wave operator. The distributional formulation goes back to J. Dieudonné and J. Horváth.The analytic continuation of these distribution-valued functions yields convolution groups and fundamental solutions of the corresponding linear partial differential operators with constant coefficients. The convolvability and the convolution of distributions and, in particular, of quasihomogeneous distributions are investigated systematically. In contrast to most textbooks on distribution theory, the general concept of convolution of distributions is employed. It was defined by L. Schwartz and further analyzed by R. Shiraishi and J. Horváth.The authors Norbert Ortner (* 1945, Vorarlberg) and Peter Wagner (* 1956, Tirol) are well-known researchers in the fields of Distribution Theory and Partial Differential Equations. The latter is professor for mathematics at the Technical Faculty, the first one was professor for mathematics at the Faculty of Mathematics, Computer Science and Physics of the Innsbruck University.