This volume presents self-contained survey articles on modern research areas written by experts in their fields. The topics are located at the interface of spectral theory, theory of partial differential operators, stochastic analysis, and mathematical physics. The articles are accessible to graduate students and researches from other fields of mathematics or physics while also being of value to experts, as they report on the state of the art in the respective fields.

This volume collects six articles on selected topics at the frontier between partial differential equations and spectral theory, written by leading specialists in their respective field. The articles focus on topics that are in the center of attention of current research, with original contributions from the authors. They are written in a clear expository style that makes them accessible to a broader audience. The articles contain a detailed introduction and discuss recent progress, provide additional motivation, and develop the necessary tools. Moreover, the authors share their views on future developments, hypotheses, and unsolved problems.

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."

A beautiful interplay between probability theory (Markov processes, martingale theory) on the one hand and operator and spectral theory on the other yields a uniform treatment of several kinds of Hamiltonians such as the Laplace operator, relativistic Hamiltonian, Laplace-Beltrami operator, and generators of Ornstein-Uhlenbeck processes. For such operators regular and singular perturbations of order zero and their spectral properties are investigated.
A complete treatment of the Feynman-Kac formula is given. The theory is applied to such topics as compactness or trace class properties of differences of Feynman-Kac semigroups, preservation of absolutely continuous and/or essential spectra and completeness of scattering systems.
The unified approach provides a new viewpoint of and a deeper insight into the subject. The book is aimed at advanced students and researchers in mathematical physics and mathematics with an interest in quantum physics, scattering theory, heat equation, operator theory, probability theory and spectral theory.

This volume contains the proceedings of "PDE 2000", the international conference on partial differential equations held July 24 -28, 2000, in Clausthal. The confer- ence took place during the EXPO 2000 and was sponsored by the Land Nieder- sachsen, the Deutsche Forschungsgemeinschaft, the Bergstadt Clausthal-Zellerfeld and the Kreissparkasse Clausthal-Zellerfeld. This conference continues a series: Ludwigfelde 1976, Reinhardsbrunn 1985, Holz- hau 1988, Breitenbrunn 1990, Lambrecht 1991 (proceedings in Operator Theory: Advances and Applications, Vol. 57, Birkhauser Verlag 1992), Potsdam 1992 and 1993, Holzhau 1994 (proceedings in Operator Theory: Advances and Applications, Vol. 78, Birkhauser Verlag 1995), Caputh 1995 and Potsdam 1996 (proceedings in Mathematical Research, Vol. 100, Akademie Verlag 1997). The intention of the organizers was to bring together specialists from different areas of modern analysis, mathematical physics and geometry, to discuss not only the recent progress in their own fields but also the interaction between these fields. The special topics of the conference were spectral and scattering theory, semiclas- sical and asymptotic analysis, pseudodifferential operators and their relation to geometry, as well as partial differential operators and their connection to stochas- tic analysis and to the theory of semigroups. The scientific advisory board of the conference in Clausthal consisted of M. Ben- Artzi (Jerusalem), Chen Hua (Peking), M. Demuth (Clausthal), T. Ichinose (Kanazawa), 1. Rodino (Thrin), B.-W. Schulze (Potsdam) and J. Sjostrand (Paris).

Partial differential equations constitute an integral part of mathematics. They lie at the interface of areas as diverse as differential geometry, functional analysis, or the theory of Lie groups and have numerous applications in the applied sciences. A wealth of methods has been devised for their analysis. Over the past decades, operator algebras in connection with ideas and structures from geometry, topology, and theoretical physics have contributed a large variety of particularly useful tools. One typical example is the analysis on singular configurations, where elliptic equations have been studied successfully within the framework of operator algebras with symbolic structures adapted to the geometry of the underlying space. More recently, these techniques have proven to be useful also for studying parabolic and hyperbolic equations. Moreover, it turned out that many seemingly smooth, noncompact situations can be handled with the ideas from singular analysis. The three papers at the beginning of this volume highlight this aspect. They deal with parabolic equations, a topic relevant for many applications. The first article prepares the ground by presenting a calculus for pseudo differential operators with an anisotropic analytic parameter. In the subsequent paper, an algebra of Mellin operators on the infinite space-time cylinder is constructed. It is shown how timelike infinity can be treated as a conical singularity.

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).

The spectral theory of SchrAdinger operators, in particular those with random potentials, continues to be a very active field of research. This work focuses on various known criteria in the spectral theory of selfadjoint operators in order to identify the spectrum and its components A la Lebesgue decomposition.

Key features and topics:

* Well-developed exposition of criteria that are especially useful in determining the spectra of deterministic and random SchrAdinger operators occurring in quantum theory

* Systematically uses measures and their transforms (Fourier, Borel, wavelet) to present a unifying theme

* Establishes criteria for identifying the spectrum

* Examines a series of applications to show point spectrum and continuous spectrum in some models of random operators

* Presents a series of spectral-theoretic results for the perturbed operators introduced in the earlier chapters with examples of localization and delocalization in the theory of disordered systems

* Presents modern criteria (using wavelet transform, eigenfunction decay) that could be used to do spectral theory

* Unique work in book form combining the presentation of the deterministic and random cases, which will serve as a platform for further research activities

This concise unified presentation is aimed at graduate students and researchers working in the spectral theory of SchrAdinger operators with either fixed or random potentials in particular. However, given the large gap that this book fills in the literature, it will serve a wider audience of mathematical physicists in its contribution to works in spectral theory.

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."

A beautiful interplay between probability theory (Markov processes, martingale theory) on the one hand and operator and spectral theory on the other yields a uniform treatment of several kinds of Hamiltonians such as the Laplace operator, relativistic Hamiltonian, Laplace-Beltrami operator, and generators of Ornstein-Uhlenbeck processes. For such operators regular and singular perturbations of order zero and their spectral properties are investigated.
A complete treatment of the Feynman-Kac formula is given. The theory is applied to such topics as compactness or trace class properties of differences of Feynman-Kac semigroups, preservation of absolutely continuous and/or essential spectra and completeness of scattering systems.
The unified approach provides a new viewpoint of and a deeper insight into the subject. The book is aimed at advanced students and researchers in mathematical physics and mathematics with an interest in quantum physics, scattering theory, heat equation, operator theory, probability theory and spectral theory.

This volume collects six articles on selected topics at the frontier between partial differential equations and spectral theory, written by leading specialists in their respective field. The articles focus on topics that are in the center of attention of current research, with original contributions from the authors. They are written in a clear expository style that makes them accessible to a broader audience. The articles contain a detailed introduction and discuss recent progress, provide additional motivation, and develop the necessary tools. Moreover, the authors share their views on future developments, hypotheses, and unsolved problems.

In diesem wertvollen Ratgeber bieten erfahrene Optionsschein-Spezialisten gut umsetzbare Anlagestrategien aus der Praxis fur alle Formen von Optionsscheinen. Inklusive zahlreicher Beispiele und Checklisten, Informationsquellen und einem umfangreichen Glossar."

Fachzeitschriften und Wirtschaftszeitungen haben in letzter Zeit in der Berichterstattung und Analyse von Finanzinnovationen einen neuen Schwerpunkt gefunden. Dabei erfolgen die Anderungen so schnell, daB es selbst Bankpraktikem nicht mehr moglich ist, die neuen Instrumente en detail zu analysieren und zu bewerten. Bisherige Monographien oder Sammelbande berichten entweder zu breit oder selektiv tiber einzelne Instrumente. Daher ist es das Anliegen der Arbeit von Michael Demuth, eine systematische und detaillierte Beschreibung und Analyse von Finanzinnovationen fUr den wichtigen Bereich der Fremdkapitalbeschaffung zu geben. Die Thematik wurde von dem Verfasser im Rahmen einer sechsmona tigen freien wissenschaftlichen Arbeit am Institut fUr Betriebswirt schaftlehre der Universitat Kiel behandelt. Die Basis der Arbeit bildet das Konzept des morphologischen Kastens, wonach sich eine Entscheidungsaltemative - hier ein Finan zierungsinstrument - durch eine spezifische Kombination von Merk malen und deren Auspragungen entwickeln laBt. Ftir die Marktteilnehmer ist es femer von Bedeutung, daB der Verfasser die neuen Instrumente jeweils auch aus Sicht der Emit tenten, der Banken und der Kapitalanleger beurteilt. Somit ntitzt diese Schrift nicht nur den Studierenden, sondem vor all em auch der Praxis. Reinhart Schmidt KieL im Juli 1988 Inhaltsverzeichnis Abbildungsverzeiehnis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XII Abkiirzungsverzeiehnis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XIV 1. Grundlagen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1. Zielsetzung und Aufbau der Arbeit. . . . . . . . . . . . . . . . . . . . . 1 1.2. Begriffssystem der Finanzinnovationen . . . . . . . . . . . . . . . . . 3 1.3. Teehnik der Finanzinnovationen . . . . . . . . . . . . . . . . . . . . . . . 9 2. Instrumente mit fester Verzinsung. . . . . . . . . . . . . . . . . . . . . . 11 2.1. Zerobonds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Finanzierungskonzept. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.1."

This volume highlights the analysis on noncompact and singular manifolds within the framework of the cone calculus with asymptotics. The three papers at the beginning deal with parabolic equations, a topic relevant for many applications. The first article presents a calculus for pseudodifferential operators with an anisotropic analytic parameter. The subsequent paper develops an algebra of Mellin operators on the infinite space-time cylinder. It is shown how timelike infinity can be treated as a conical singularity. In the third text - the central article of this volume - the authors use these results to obtain precise information on the long-time asymptotics of solutions to parabolic equations and to construct inverses within the calculus. There follows a factorization theorem for meromorphic symbols: It is proven that each of these can be decomposed into a holomorphic invertible part and a smoothing part containing all the meromorphic information. It is expected that this result will be important for applications in the analysis of nonlinear hyperbolic equations. The final article addresses the question of the coordinate invariance of the Mellin calculus with asymptotics.