This volume is essentially a self-contained presentation of the theory of reproducing kernels in connection with integral transforms in the framework of Hilbert spaces. It is a general and fundamental concept and a potentially powerful theory combined with the integral transforms. A variety of concrete results of its application are given systematically for isometrical identities and inversion formulas for various typical integral transforms, best approximation theories of functions, analytic extension formulas, real inversion formulas for the Laplace transform, inverse source problems,...

Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis. Retaining its concise presentation but offering streamlined analyses and expanded coverage of important examples and applications, Elliptic Operators, Topology, and Asymptotic Methods, Second Edition introduces the ideas surrounding the heat equation proof of the Atiyah-Singer index theorem.
The author builds towards proof of the Lefschetz formula and...

Top researchers in optimization and control from around the world gathered in Detroit for the 18th annual IFIP TC7 Conference on Systems Modelling and Optimization held in July 1997. The papers offered in this volume were selected from among the 250 plenary, invited, and contributed works presented at the conference. The editors chose these papers to represent the myriad and diverse range of topics within the field -in theory and applications-and to disseminate important new results.
The editors have organized the book into seven sections:

Distributed Parameter...

Questions regarding the interplay of nonlinearity and the creation and propagation of singularities arise in a variety of fields-including nonlinear partial differential equations, noise-driven stochastic partial differential equations, general relativity, and geometry with singularities. A workshop held at the Erwin-Schrodinger International Institute for Mathematical Physics in Vienna investigated these questions and culminated in this volume of invited papers from experts in the fields of nonlinear partial differential equations, structure theory of generalized functions, geometry and...

The fruit of a conference that gathered seven very active researchers in the field, Combinatorial Design and their Applications presents a wide but representative range of topics on the non-geometrical aspects of design theory. By concentrating on a few important areas, the authors succeed in providing greater detail in these areas in a more complete and accessible form. Through their contributions to this collection, they help fill a gap in the available combinatorics literature.
The papers included in this volume cover recent developments in areas of current interest, such as difference...

Boundary element methods relate to a wide range of engineering applications, including fluid flow, fracture analysis, geomechanics, elasticity, and heat transfer. Thus, new results in the field hold great importance not only to researchers in mathematics, but to applied mathematicians, physicists, and engineers.

A two-day minisymposium Mathematical Aspects of Boundary Element Methods at the IABEM conference in May 1998 brought together top rate researchers from around the world, including Vladimir Maz ya, to whom the conference was dedicated. Focusing on the mathematical and...

The proceedings of a satellite conference of the 1998 International Mathematical Congress. In it, leading specialists on partial differential equations, calculus of variations, and numerical analysis present results, applications, and advances in numerical methods in these fields. Conference organizers chose the contributors to bring together the scientists best able to present a complex view of problems, starting from the modelling, passing through the mathematical treatment, and ending with numerical realization. The applications discussed include fluid dynamics, semiconductor technology,...

The calculus of variations is a classical area of mathematical analysis-300 years old-yet its myriad applications in science and technology continue to hold great interest and keep it an active area of research. These two volumes contain the refereed proceedings of the international conference on Calculus of Variations and Related Topics held at the Technion-Israel Institute of Technology in March 1998. The conference commemorated 300 years of work in the field and brought together many of its leading experts.
The papers in the first volume focus on critical point theory and differential...

Working with mathematical models today requires in-depth knowledge of recent methods developed for solving nonlinear differential equations. Keeping abreast of these developments is the goal of the regular meetings of nonlinear analysts held in the Czech Republic, the most recent of which formed the basis of this volume.
The subject addressed by these authors is the theory of nonlinear differential equations, with focus on the quasilinear elliptic differential equations of the degenerate type. Their topics include:

The Proceedings of the Fifth International Conference on Integral Methods in Science and Engineering, form a collection of papers addressing the solution of mathematical problems from various physical domains by integral methods in conjunction with various approximation schemes. Written by acknowledged experts, these peer-reviewed papers offer recent developments in both theory and application valuable to applied mathematicians, engineers, and physicists.