Pseudodifferential methods are central to the study of partial differential equations, because they permit an "algebraization." A replacement of compositions of operators in n-space by simpler product rules for thier symbols. The main purpose of this book is to set up an operational calculus for operators defined from differential and pseudodifferential boundary values problems via a resolvent construction. A secondary purposed is to give a complete treatment of the properties of the calculus of pseudodifferential boundary problems with transmission, both the first version by...
Pseudodifferential methods are central to the study of partial differential equations, because they permit an "algebraization." A replacement of co...
The deep and original ideas of Norman Levinson have had a lasting impact on fields as diverse as differential & integral equations, harmonic, complex & stochas- tic analysis, and analytic number theory during more than half a century. Yet, the extent of his contributions has not always been fully recognized in the mathematics community. For example, the horseshoe mapping constructed by Stephen Smale in 1960 played a central role in the development of the modern theory of dynami- cal systems and chaos. The horseshoe map was directly stimulated by Levinson's research on forced periodic...
The deep and original ideas of Norman Levinson have had a lasting impact on fields as diverse as differential & integral equations, harmonic, complex ...
20. Pattern recognition and statistical learning theory (the theory of support vector machines). See 40], 58]. In this last volume we refer in particular to the papers 63] and 64]. Since this topic is maybe less known to the operator theory community we mention that the support vector method is a general approach to function estimation problems. See 63, p. 26]. We note that the above list and the given references are by no way exhaustive. We refer to the first section of the paper of S. Saitoh in the present volume for another (and mainly different) list of topics where reproducing...
20. Pattern recognition and statistical learning theory (the theory of support vector machines). See 40], 58]. In this last volume we refer in parti...
The monograph is devoted to the study of functional equations with the transformed argument on the real line and on the unit circle. Such equations systematically arise in dynamical systems, differential equations, probabilities, singularities of smooth mappings, and other areas. The purpose of the book is to present modern methods and new results in the subject, with an emphasis on a connection between local and global solvability. The general concepts developed in the book are applicable to multidimensional functional equations. Some of the methods are presented for the first time in the...
The monograph is devoted to the study of functional equations with the transformed argument on the real line and on the unit circle. Such equations...
This volume contains the contributions of participants of the conference "Optimal Control of Partial Differential Equations" which, under the chairmanship of the editors, took place at the Mathematisches Forschungsinstitut Oberwolfach from May 18 to May 24, 1986. The great variety of topics covered by the contributions strongly indicates that also in the future it will be impossible to develop a unifying control theory of partial differential equations. On the other hand, there is a strong tendency to treat prob- lems which are directly connected to practical applications. So this volume...
This volume contains the contributions of participants of the conference "Optimal Control of Partial Differential Equations" which, under the chairman...
This volume focuses on recent developments in non-linear and hyperbolic equations. It will be a most valuable resource for researchers in applied mathematics, the theory of wavelets, and in mathematical and theoretical physics. Nine up-to-date contributions have been written on invitation by experts in the respective fields. The book is the third volume of the subseries "Advances in Partial Differential Equations."
This volume focuses on recent developments in non-linear and hyperbolic equations. It will be a most valuable resource for researchers in applied m...
George Boole (1815-1864) is well known to mathematicians for his research and textbooks on the calculus, but his name has spread world-wide for his innovations in symbolic logic and the development and applications made since his day. The utility of "Boolean algebra" in computing has greatly increased curiosity in the nature and extent of his achievements. His work is most accessible in his two books on logic, "A mathematical analysis of logic" (1947) and "An investigation of the laws of thought" (1954). But at various times he wrote manuscript essays, especially after the publication of the...
George Boole (1815-1864) is well known to mathematicians for his research and textbooks on the calculus, but his name has spread world-wide for his in...
This book contains the historical development of the seminal paper of Adolf Hurwitz, professor in mathematics at ETH (1892 1919), and its impact on other fields. The major emphasis, however, is on modern results in stability theory and its application in the theory of control and numerics. In particular, stability of the following problems is treated: linear, nonlinear and time-dependent systems, discretizations of ordinary and partial differential equations, systems with time delay on multidimensional systems. In addition robust stability, pole placement and problems related to the stability...
This book contains the historical development of the seminal paper of Adolf Hurwitz, professor in mathematics at ETH (1892 1919), and its impact on ot...
This book is based on lecture notes of a seminar of the Deutsche Mathematiker Vereinigung held by the authors at Oberwolfach from April 2 to 8, 1995. It gives an introduction to the classification theory and geometry of higher dimensional complex-algebraic varieties, focusing on the tremendeous developments of the sub ject in the last 20 years. The work is in two parts, with each one preceeded by an introduction describing its contents in detail. Here, it will suffice to simply ex plain how the subject matter has been divided. Cum grano salis one might say that Part 1 (Miyaoka) is more...
This book is based on lecture notes of a seminar of the Deutsche Mathematiker Vereinigung held by the authors at Oberwolfach from April 2 to 8, 1995. ...
Disordered systems are statistical mechanics models in random environments. This work deals with the equilibrium properties of a few chosen examples of disordered Ising models. It considers two main types of systems: disordered ferromagnets and spin glasses.
Disordered systems are statistical mechanics models in random environments. This work deals with the equilibrium properties of a few chosen examples o...
