springer basel springer basel apr 2011 (4 Ergebnisse)

Taschenbuch. Zustand: Neu. Neuware -'Numerische Mathematik', aufgeteilt in zwei Bände, ist eine Einführung in die Numerische Mathematik anhand von Differentialgleichungsproblemen. Gegliedert nach elliptischen, parabolischen und hyperbolischen Differentialgleichungen wird zunächst jeweils die Diskretisierung solcher Probleme besprochen. Als Diskretisierungstechniken stehen Finite-Elemente-Methoden im Raum und (partitionierte) Runge-Kutta-Methoden in der Zeit im Vordergrund. Die diskretisierten Gleichungen dienen als Motivation zur Diskussion von Methoden für endlichdimensionale lineare und nichtlineare Gleichungen, die anschließend als eigenständige Themen behandelt werden. Auf diese Weise wird versucht, nicht nur ein einführendes sondern auch ein in sich abgeschlossenes Bild der Numerischen Mathematik, zumindest in einem zentralen Aufgabenbereich, zu vermitteln.Der zweite Band setzt mit der Diskussion parabolischer und hyperbolischer Anfangsrandwertprobleme fort. Die durch Semi-Diskretisierung im Raum entstehenden Anfangswertprobleme dienen als Einstieg und Motivation der anschließenden Behandlung allgemeiner Anfangswertprobleme gewöhnlicher Differentialgleichungen erster und zweiter Ordnung. Schließlich werden die für diese allgemeinen Problemstellungen erarbeiteten Erkenntnisse auf semi-diskretisierte parabolische und hyperbolische Probleme angewendet.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 168 pp. Deutsch.

Buch. Zustand: Neu. Neuware -This book provides a systematic development of the Rubio de Francia theory of extrapolation, its many generalizations and its applications to one and two-weight norm inequalities.The book is based upon a new and elementary proof of the classical extrapolation theorem that fully develops the power of the Rubio de Francia iteration algorithm.This technique allows us to give a unified presentation of the theory and to give important generalizations to Banach function spaces and to two-weight inequalities.We provide many applications to the classical operators of harmonic analysis to illustrate our approach, giving new and simpler proofs of known results and proving new theorems.The book is intended for advanced graduate students and researchers in the area of weighted norm inequalities, as well as for mathematicians who want to apply extrapolation to other areas such as partial differential equations.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 296 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -The discoveries of the last decades have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: symplectic topology. Surprising rigidity phenomena demonstrate that the nature of symplectic mappings is very different from that of volume preserving mappings. This raises new questions, many of them still unanswered. On the other hand, analysis of an old variational principle in classical mechanics has established global periodic phenomena in Hamiltonian systems. As it turns out, these seemingly different phenomena are mysteriously related. One of the links is a class of symplectic invariants, called symplectic capacities. These invariants are the main theme of this book, which includes such topics as basic symplectic geometry, symplectic capacities and rigidity, periodic orbits for Hamiltonian systems and the action principle, a bi-invariant metric on the symplectic diffeomorphism group and its geometry, symplectic fixed point theory, the Arnold conjectures and first order elliptic systems, and finally a survey on Floer homology and symplectic homology.The exposition is self-contained and addressed to researchers and students from the graduate level onwards.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 356 pp. Englisch.

Buch. Zustand: Neu. Neuware -This monograph gives a systematic account of the theory of vector-valued Laplace transforms, ranging from representation theory to Tauberian theorems. In parallel, the theory of linear Cauchy problems and semigroups of operators is developed completely in the spirit of Laplace transforms. Existence and uniqueness, regularity, approximation and above all asymptotic behaviour of solutions are studied. Diverse applications to partial differential equations are given. The book contains an introduction to the Bochner integral and several appendices on background material. It is addressed to students and researchers interested in evolution equations, Laplace and Fourier transforms, and functional analysis. The second edition contains detailed notes on the developments in the last decade. They include, for instance, a new characterization of well-posedness of abstract wave equations in Hilbert space due to M. Crouzeix. Moreover new quantitative results on asymptotic behaviour of Laplace transforms have been added. The references are updated and some errors have been corrected.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 552 pp. Englisch.