Bücher veröffentlicht von Springer Basel

Semilinear elliptic equations play an important role in many areas of mathematics and its applications to other sciences. This book presents a wealth of modern methods to solve such equations. Readers of this exposition will be advanced students and researchers in mathematics, physics and other.

Kurt Goedel, together with Bertrand Russell, is the most important name in logic, and in the foundations and philosophy of mathematics of this century.

In recent years many researchers in material science have focused their attention on the study of composite materials, equilibrium of crystals and crack distribution in continua subject to loads.

4 Hardy-Toeplitz Operators Over Tubular Domains 267 4.

Advancements in digital sensor technology, digital image analysis techniques, as well as computer software and hardware have brought together the fields of computer vision and photogrammetry, which are now converging towards sharing, to a great extent, objectives and algorithms.

This book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be applied to the study of parabolic problems. It presents known theorems from a novel perspective and teaches how to exploit basic techniques.

Knot theory is a rapidly developing field of research with many applications, not only for mathematics. The present volume, written by a well-known specialist, gives a complete survey of this theory from its very beginnings to today's most recent research results. An indispensable book for everyone concerned with knot theory.

This distinguishes it from the theory of nonlinear contraction semigroups whose basis is a nonlinear version of the Hille Yosida theorem: the Crandall-Liggett theorem. Thus the theory of nonlinear contraction semigroups does not apply to systems, in general, since they do not allow for a maximum principle.

Andreas Floer died on May 15, 1991 an untimely and tragic death. His visions and far-reaching contributions have significantly influenced the developments of mathematics. His main interests centered on the fields of dynamical systems, symplectic geometry, Yang-Mills theory and low dimensional topology. Motivated by the global existence problem of periodic solutions for Hamiltonian systems and starting from ideas of Conley, Gromov and Witten, he developed his Floer homology, providing new, powerful methods which can be applied to problems inaccessible only a few years ago. This volume opens with a short biography and three hitherto unpublished papers of Andreas Floer. It then presents a collection of invited contributions, and survey articles as well as research papers on his fields of interest, bearing testimony of the high esteem and appreciation this brilliant mathematician enjoyed among his colleagues. Authors include: A. Floer, V.I. Arnold, M. Atiyah, M. Audin, D.M. Austin, S.M. Bates, P.J. Braam, M. Chaperon, R.L. Cohen, G. Dell' Antonio, S.K. Donaldson, B. D'Onofrio, I. Ekeland, Y. Eliashberg, K.D. Ernst, R. Finthushel, A.B. Givental, H. Hofer, J.D.S. Jones, I. McAllister, D. McDuff, Y.-G. Oh, L. Polterovich, D.A. Salamon, G.B. Segal, R. Stern, C.H. Taubes, C. Viterbo, A. Weinstein, E. Witten, E. Zehnder

The theory of integral equations has been an active research field for many years and is based on analysis, function theory, and functional analysis.

The book is an outgrowth of the international conference "Centennial Hurwitz on Stability Theory" which was held to honor Adolf Hurwitz, whose arti cle on the location of roots of a polynomial was published one hundred years ago.

Sub-Riemannian geometry (also known as Carnot geometry in France, and non-holonomic Riemannian geometry in Russia) has been a full research domain for fifteen years, with motivations and ramifications in several parts of pure and applied mathematics, namely:¿ control theory ¿ classical mechanics ¿ Riemannian geometry (of which sub-Riemannian geometry constitutes a natural generalization, and where sub-Riemannian metrics may appear as limit cases) ¿ diffusion on manifolds ¿ analysis of hypoelliptic operators ¿ Cauchy-Riemann (or CR) geometry.Although links between these domains had been foreseen by many authors in the past, it is only in recent years that sub- Riemannian geometry has been recognized as a possible common framework for all these topics. This book provides an introduction to sub-Riemannian geometry and presents the state of the art and open problems in the field. It consists of five coherent and original articles by the leading specialists:¿ André Bellaïche: The tangent space in sub-Riemannian geometry ¿ Mikhael Gromov: Carnot-Carathéodory spaces seen from within ¿ Richard Montgomery: Survey of singular geodesics ¿ Héctor J. Sussmann: A cornucopia of four-dimensional abnormal sub-Riemannian minimizers ¿ Jean-Michel Coron: Stabilization of controllable systems

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.

Die Akustik ist ein Gebiet, das erstaunlicherweise in der wissenschaftshistorischen Literatur nur relativ selten zu finden ist. Darstellungen langerer Epochen in der Entwicklung dieses Fachgebietes haben noch groBeren Seltenheitswert. Nach dem Zweiten Weltkrieg erschien bisher lediglich F.V. HUNTS "Origins in acoustics", das im wesentlichen die Zeitepoche von der Antike bis NEWTON beschreibt. Ein Buch, das in gewisser Weise aIs eine Fortsetzung betrachtet werden kann, ist CANNON/DoSTROVSKYS "The evolution of dynamics: Vibration theory from 1687 to 1742". Es setzt jedoch gemlill seinem Titel ganz bestimmte Akzente. Mit NEWTONS "Principia" von 1687 beginnt eine Periode ausgesprochen theoretischer Forschung auf dem Gebiet der Akustik, fUr die Namen wie z.B. TAYLOR, SAUVEUR, EULER, D'ALEMBERT, JOHANN und DANIEL BERNOULLI Zeugnis ablegen. Dieses Uberwiegen der Theorie wird 1787 mit dem Auftreten CHLADNIS wieder zugunsten des Experiments verschoben. Da es tiber die Tatigkeit der eben genannten Forscher bereits einige ausfUhrliche DarsteIlungen gibt, beginnt die detaillierte Betrachtung in diesem Buch erst im Erscheinungsjahr von CHLADNIS Erstlingswerk. Ziel dieses Buches ist es, nicht nur die akustischen Arbeiten CHLADNIS zu beschreiben, sondem auch seinen Einflull auf die Forschung bis in die Mitte des 19.

Incomplete second order linear differential equations in Banach spaces as well as first order equations have become a classical part of functional analysis. Special emphasis is placed on new surprising effects arising for complete second order equations which do not take place for first order and incomplete second order equations.

"Functional Analysis" is a comprehensive, 2-volume treatment of a subject lying at the core of modern analysis and mathematical physics. Volume II moves on to more advanced topics including unbounded operators, spectral decomposition, expansion in generalized eigenvectors, rigged spaces, and partial differential operators.

In 1992, a group of scientists including molecular biologists, microbiologists, population biolo­ gists, ecologists, human geneticists, moral philosophers and others met discussing the state of affairs regarding the deliberate or unintentional release of genetically modified organisms. The proceedings of this meeting were subsequently published by Birkhauser Verlag as Transgenic Organisms: Risk Assessment of Deliberate Release (K. Wohrmann and J. Tomiuk). Since then we have gained many new insights that are also worthy of discussion. And although other equally important scientific views on the release of genetically modified organisms exist, we have mainly concentrated on aspects of population biology and evolution. The results of a second meeting in 1995 are summarized here. We are grateful to colleagues and friends for their help in the translation, correction and review of the authors' contributions. We especially want to thank Jutta Bachmann, Donna Devine, Diana von Finck, Friedrich Laplace, Volker Loeschcke, Rolf Lorenz, Dave Parker and Trevor Petney. A grant (BMFT N' 0311035) from the Ministerium fUr Forschung und Technologie der Bundesrepublik Deutschland again made possible the continuation of this cooperative endeavour.

Continuing the Respiratory Pharmacology and Pharmacotherapy series, this volume explores the pathophysiology and therapy of rhinitis. The various causes and the types of rhinitis - such as allergic, vasomotor, and infectious - are discussed as are the treatments available (pharmacotherapy, immunotherapy, surgery).

The subject of this book is about the ubiquity of the Schur parameters, whose introduction goes back to a paper of I. Schur in 1917 concerning an interpolation problem of C. Caratheodory. What followed there appears to be a truly fascinating story which, however, should be told by a professional historian. Here we provide the reader with a simplified version, mostly related to the contents of the book. In the twenties, thf~ theory of orthogonal polynomials on the unit circle was developed by G. Szego and the formulae relating these polynomials involved num­ bers (usually called Szego parameters) similar to the Schur parameters. Mean­ while, R. Nevanlinna and G. Pick studied the theory of another interpolation problem, known since then as the Nevanlinna-Pick problem, and an algorithm similar to Schur's one was obtained by Nevanlinna. In 1957, Z. Nehari solved OO an L problem which contained both Caratheodory-Schur and Nevannlina-Pick problems as particular cases. Apparently unrelated work of H. Weyl, J. von Neu­ mann and K. Friedericks concerning selfadjoint extensions of symmetric operators was connected to interpolation by M. A. Naimark and M. G Krein using some gen­ eral dilation theoretic ideas. Classical moment problems, like the trigonometric moment and Hamburger moment problems, were also related to these topics and a comprehensive account of what can be called the classical period has appeared in the monograph of M. G. Krein and A. A. Nudelman, [KN].

This volume arises from the contributions presented at the MEGA 94 Con­ ference (Metodos Efectivos en Geomctria Algebraica = Effective Methods in Algebraic Geometry), held at the University of Cantabria (Santander, Spain) April 59, 1994. Previous sessions of this biannual conference had taken place in Castiglioncello (Livorno, Italy, 1990) and in Nice (France, 1992) and the cor­ responding proceedings have been published in the Birkhauser series Progress in Mathematics. volumes no. 94 and 109, respectively. The present collection consists of twenty articles involvillg miscellaneous topics concerning algorithms in algebra, algebraic geometry and related appli­ cations. Fourteen of these papers correspond to the contents of the Conference's regular scientific program and have been selected, by the MEGA Committee, from the submitted contributions after a very rigorous refereeing procedure entailing an average of three independent reports per paper and two Program Committee panel discussions before and after the Conference. The remaining six papers (by S. Beck & M. Kreuzer, M. Bronstein, E. V. Flvnn. 1. Itenberg, J.-P. Merlet and 1\1. Seppala) correspond to invited talks and have also been subject to a post-conference refereeing procedure.

This book is devoted to a new direction in linear algebra and operator theory that deals with the invariants of partially specified matrices and operators, and with the spectral analysis of their completions. The theory developed centers around two major problems concerning matrices of which part of the entries are given and the others are unspecified. The first is a classification problem and aims at a simplification of the given part with the help of admissible similarities. The results here may be seen as a far reaching generalization of the Jordan canonical form. The second problem is called the eigenvalue completion problem and asks to describe all possible eigenvalues and their multiplicities of the matrices which one obtains by filling in the unspecified entries. Both problems are also considered in an infinite dimensional operator framework. A large part of the book deals with applications to matrix theory and analysis, namely to stabilization problems in mathematical system theory, to problems of Wiener-Hopf factorization and interpolation for matrix polynomials and rational matrix functions, to the Kronecker structure theory of linear pencils, and to non­ everywhere defined operators. The eigenvalue completion problem has a natural associated inverse, which appears as a restriction problem. The analysis of these two problems is often simpler when a solution of the corresponding classification problem is available.

The Bochner-Martinelli integral representation for holomorphic functions or'sev eral complex variables (which has already become classical) appeared in the works of Martinelli and Bochner at the beginning of the 1940's.

This volume contains the proceedings of the International Conference on "Par­ tial Differential Equations" held in HolzhaujErzgebirge, Germany, July 3~9, 1994. The conference was sponsored by the Max-Planck-Gesellschaft, the Deutsche For­ schungsgemeinschaft, the Land Brandenburg and the Freistaat Sachsen. It was initiated by the Max-Planck-Research Group "Partielle Differential­ gleichungen und Komplexe Analysis" at the University of Potsdam as one of the annual meetings of the research group. This conference is part of a series begun by the former Karl-Weierstraf3-Institute of Mathematics in Berlin, with the confer­ ences in Ludwigsfelde 1976, Reinhardsbrunn 1985, Holzhau 1988 (proceedings in the Teubner Texte zur Mathematik 112, Teubner-Verlag 1989), Breitenbrunn 1990 (proceedings in the Teubner Texte zur Mathematik 131, Teubner-Verlag 1992), and Lambrecht 1991 (proceedings in Operator Theory: Advances and Applications, Vol. 57, Birkhiiuser Verlag 1992); subsequent conferences took place in Potsdam in 1992 and 1993 under the auspices of the Max-Planck-Research Group "Partielle Differentialgleichungen und Komplexe Analysis" at the University of Potsdam. It was the intention of the organizers to bring together specialists from differ­ ent areas of modern analysis, geometry and mathematical physics to discuss not only recent progress in the respective disciplines but also to encourage interaction between these fields. The scientific advisory board of the Holzhau conference consisted of S. Al­ beverio (Bochum), L. Boutet de Monvel (Paris), M. Demuth (Clausthal), P. Gilkey (Eugene), B. Gramsch (Mainz), B. Helffer (Paris), S.T. Kuroda (Tokyo), B.-W. Schulze (Potsdam).

This is the sixth published volume of the Israel Seminar on Geometric Aspects of Functional Analysis. The previous volumes are 1983-84 published privately by Tel Aviv University 1985-86 Springer Lecture Notes, Vol. 1267 1986-87 Springer Lecture Notes, Vol. 1317 1987-88 Springer Lecture Notes, Vol. 1376 1989-90 Springer Lecture Notes, Vol. 1469 As in the previous vC!lumes the central subject of -this volume is Banach space theory in its various aspects. In view of the spectacular development in infinite-dimensional Banach space theory in recent years (like the solution of the hyperplane problem, the unconditional basic sequence problem and the distortion problem in Hilbert space) it is quite natural that the present volume contains substantially more contributions in this direction than the previous volumes. This volume also contains many important contributions in the "traditional directions" of this seminar such as probabilistic methods in functional analysis, non-linear theory, harmonic analysis and especially the local theory of Banach spaces and its connection to classical convexity theory in IRn. The papers in this volume are original research papers and include an invited survey by Alexander Olevskii of Kolmogorov's work on Fourier analysis (which was presented at a special meeting on the occasion of the 90th birthday of A. N. Kol­ mogorov). We are very grateful to Mrs. M. Hercberg for her generous help in many directions, which made the publication of this volume possible. Joram Lindenstrauss, Vitali Milman 1992-1994 Operator Theory: Advances and Applications, Vol.

"Stress-Inducible Cellular Responses" are essential for survival of cells of all species under adverse conditions. At the molecular level this is ac­ complished by a number of essential proteins all of which are involved in various aspects of cellular homeostasis through protective or adaptive func­ tions. Interestingly, molecules such as heat shock proteins have properties as molecular chaperones and are involved in multiple stages of a protein biogenesis beginning with synthesis and involvement in the subsequent events of folding, translocation, and degradation. Heat shock proteins have a critical role to stabilize folding intermediates and to prevent protein aggregation. In addition, stress-proteins serve as targets for immune re­ sponses in immune homeostasis and during infections. The term Stress Response reflects the rapid growth and breadth of this field which includes the molecular and cellular response to drugs, UV irra­ diation, oxidative stress, and environmental toxins. Radical scavengers such as superoxide dismutases and inducible regulatory proteins of metall­ ic ion status such as ferritin and protein disulfide isomerases are also con­ sidered within the frame of stress proteins and represent a new and growing class of stress responses.

New methods for solving classical problems in the theory of nonlinear operator equations (solvability, multiple solutions, bifurcations, nonlinear resonance, potential methods, etc) are introduced and discussed. In particular, the problem on forced periodic oscillations is considered for equations arising in control theory.

Der Astronom F.W. Bessel gilt zusammen mit dem Mathematiker C.G.J. Jacobi und dem Physiker Franz Neumann als Begründer der sogenannten 'Königsberger Schule', die auf die Universitäten in Deutsch- land, aber auch in Russland und im gesamten osteuropäischen Raum, einen grossen Einfluss hatte. Als Autodidakt erwarb sich Bessel schon in jungen Jahren mit seinen astronomischen Arbeiten die Anerkennung der führenden Gelehrten seiner Zeit. Nachdem er als Professor an die Albertina nach Königsberg berufen worden war, erhielt er bereits mit 27 Jahren auf Betreiben von Gauss die Ehren- doktorwürde der Universität Göttingen. Ihm wurde die Planung und der Bau der Königsberger Sternwarte übertragen, die sich unter seiner Leitung zu einem internationalen Zentrum der Astronomie entwickelte. Bessel leistete aber nicht nur in der Astronomie und der Geodäsie Bedeutendes, sondern auch in der Theoretischen Mathematik. Diese Biographie beschränkt sich nicht auf die Schilderung der wissenschaftlichen Leistungen Bessels, sondern stellt ihn auch als Mensch und Persönlichkeit vor. Besondere Aufmerksamkeit widmet das Buch den engen wissenschaftlichen und persönlichen Be- ziehungen, die Bessel, nachdem er schon in jungen Jahren in die Petersburger Akademie aufgenommen worden war, zur russischen Wissenschaft und zu den russischen Wissenschaftlern entwickelt hat. Engagiert und lebendig schildert der Autor Bessels Lebensgeschichte und versucht, Bessels zahlreiche, weitgespannte wissenschaftliche Arbeiten und Leistungen auch dem Nichtfachmann verständlich und spannend darzustellen.

The aim of the present book is to propose a new algebraic approach to the study of norm stability of operator sequences which arise, for example, via discretization of singular integral equations on composed curves.