birkhäuser basel birkhäuser basel jul 1996 (3 Ergebnisse)

Buch. Zustand: Neu. Neuware -Over the past ten years, the asymptotic theory of one-parameter semigroups of operators has witnessed an explosive development. A number oflong-standing open problems have recently been solved and the theory seems to have obtained a certain degree of maturity. These notes, based on a course delivered at the University of Tiibingen in the academic year 1994-1995, represent a first attempt to organize the available material, most of which exists only in the form of research papers. If A is a bounded linear operator on a complex Banach space X, then it is an easy consequence of the spectral mapping theorem exp(tO'(A)) = O'(exp(tA)), t E JR, and Gelfand's formula for the spectral radius that the uniform growth bound of the wt family {exp(tA)h~o, i. e. the infimum of all wE JR such that II exp(tA)II :::: Me for some constant M and all t 2: 0, is equal to the spectral bound s(A) = sup{Re A : A E O'(A)} of A. This fact is known as Lyapunov's theorem. Its importance resides in the fact that the solutions of the initial value problem du(t) =A () dt u t , u(O) = x, are given by u(t) = exp(tA)x. Thus, Lyapunov's theorem implies that the expo nential growth of the solutions of the initial value problem associated to a bounded operator A is determined by the location of the spectrum of A.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 256 pp. Englisch.

Buch. Zustand: Neu. Neuware -It is well known that a wealth of problems of different nature, applied as well as purely theoretic, can be reduced to the study of elliptic equations and their eigen-values. During the years many books and articles have been published on this topic, considering spectral properties of elliptic differential operators from different points of view. This is one more book on these properties. This book is devoted to the study of some classical problems of the spectral theory of elliptic differential equations. The reader will find hardly any intersections with the books of Shubin [Sh] or Rempel-Schulze [ReSch] or with the works cited there. This book also has no general information in common with the books by Egorov and Shubin [EgShu], which also deal with spectral properties of elliptic operators. There is nothing here on oblique derivative problems; the reader will meet no pseudodifferential operators. The main subject of the book is the estimates of eigenvalues, especially of the first one, and of eigenfunctions of elliptic operators. The considered problems have in common the approach consisting of the application of the variational principle and some a priori estimates, usually in Sobolev spaces. In many cases, impor tant for physics and mechanics, as well as for geometry and analysis, this rather elementary approach allows one to obtain sharp results. 344 pp. Englisch.

Buch. Zustand: Neu. Neuware -Die Behandlung der Leguminosen in der Chemotaxonomie der Pflanzen wird mit Band XIb-1 fortgesetzt. In ihm werden die von den Caesalpinioideae und Mimosoideae bekannt gewordenen Naturstoffe im Rahmen der natürlichen Klassifikation der Familie besprochen. Der Teilband enthält über 2000 Literaturhinweise sowie ein eigenes Pflanzennamen- und Stichwortregister. Hegnauer's Chemotaxonomie is an indispensable handbook for all those scientific disciplines concerned with not only systematic botany, but all aspects of the plant world. Both text and bibliography reflect our present knowledge of the particularities of plant metabolism. The last volume of Chemotaxonomy of Plants treats Leguminosae in three parts. XIa.: General aspects. XIB-1: Phytochemistry and chemotaxonomy of Caesalpinioideae and Mimosoideae. XIb-2: Phytochemistry and chemotaxonomy of Papilionoideae (in preparation). These three volumes form a valuable tool for everyone with an interest in the Leguminosae. They are not only relevant to plant taxonomists, plant physiologists, and natural product chemists but also to ecologists, agriculturists, nutritional scientists, pharmacists, pharmacologists and ethnobotanists. The cosmopolitan Leguminosae cover approximately 600 genera and 13000 species including many economically and ethnobotanically important plants. Each of the three volumes devoted to Leguminosae contains a taxonomic index, a subject index and over 2000 references.Springer Nature c/o IBS, Benzstrasse 21, 48619 Heek 512 pp. Englisch.