birkhäuser boston birkhäuser boston jul 2005 (4 Ergebnisse)

Buch. Zustand: Neu. Neuware -This monograph examines and develops the Global Smoothness Preservation Property (GSPP) and the Shape Preservation Property (SPP) in the field of interpolation of functions. The study is developed for the univariate and bivariate cases using well-known classical interpolation operators of Lagrange, Grünwald, Hermite-Fejér and Shepard type. One of the first books on the subject, it presents interesting new results alongwith an excellent survey of past research.Key features include: potential applications to data fitting, fluid dynamics, curves and surfaces, engineering, and computer-aided geometric design presents recent work featuring many new interesting results as well as an excellent survey of past research many interesting open problems for future research presented throughout the text includes 20 very suggestive figures of nine types of Shepard surfaces concerning their shape preservation property generic techniques of the proofs allow for easy application to obtaining similar results for other interpolation operatorsThis unique, well-written text is best suited to graduate students and researchers in mathematical analysis, interpolation of functions, pure and applied mathematicians in numerical analysis, approximation theory, data fitting, computer-aided geometric design, fluid mechanics, and engineering researchers.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 164 pp. Englisch.

Buch. Zustand: Neu. Neuware -The fascinating eld of shape optimization problems has received a lot of attention in recent years, particularly in relation to a number of applications in physics and engineering that require a focus on shapes instead of parameters or functions. The goal of these applications is to deform and modify the admissible shapes in order to comply with a given cost function that needs to be optimized. In this respect the problems are both classical (as the isoperimetric problem and the Newton problem of the ideal aerodynamical shape show) and modern (re ecting the many results obtained in the last few decades). The intriguing feature is that the competing objects are shapes, i.e., domains of N R , instead of functions, as it usually occurs in problems of the calculus of va- ations. This constraint often produces additional dif culties that lead to a lack of existence of a solution and to the introduction of suitable relaxed formulations of the problem. However, in certain limited cases an optimal solution exists, due to the special form of the cost functional and to the geometrical restrictions on the class of competing domains.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 228 pp. Englisch.

Buch. Zustand: Neu. Neuware -Themainobjectiveofthisbookistogiveacollectionofcriteriaavailablein the spectral theory of selfadjoint operators, and to identify the spectrum and its components in the Lebesgue decomposition. Many of these criteria were published in several articles in di erent journals. We collected them, added some and gave some overview that can serve as a platform for further research activities. Spectral theory of Schr¿ odinger type operators has a long history; however the most widely used methods were limited in number. For any selfadjoint operatorA on a separable Hilbert space the spectrum is identi ed by looking atthetotalspectralmeasureassociatedwithit;oftenstudyingsuchameasure meant looking at some transform of the measure. The transforms were of the form f, (A)f which is expressible, by the spectral theorem, as (x)dµ (x) for some nite measureµ . The two most widely used functions were the sx 1 exponential function (x)=e and the inverse function (x)=(x z) . These functions are ¿usable¿ in the sense that they can be manipulated with respect to addition of operators, which is what one considers most often in the spectral theory of Schr¿ odinger type operators. Starting with this basic structure we look at the transforms of measures from which we can recover the measures and their components in Chapter 1. In Chapter 2 we repeat the standard spectral theory of selfadjoint op- ators. The spectral theorem is given also in the Hahn¿Hellinger form. Both Chapter 1 and Chapter 2 also serve to introduce a series of de nitions and notations, as they prepare the background which is necessary for the criteria in Chapter 3.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 232 pp. Englisch.

Buch. Zustand: Neu. Neuware - Carlos A. Berenstein has had a profound influence on scholars and practitioners alike amid a distinguished mathematical career spanning nearly four decades. His uncommon capability of adroitly moving between these parallel worlds is demonstrated by the breadth of his research interests, from his early theoretical work on interpolation in spaces of entire functions with growth conditions and residue theory to his later work on deconvolution and its applications to issues ranging from optics to the study of blood flow. This volume, which celebrates his sixtieth birthday, reflects the state-of-the-art in these areas. Original articles and survey articles, all refereed, cover topics in harmonic and complex analysis, as well as more applied work in signal processing.