Kategoria BISAC: Mathematics >> Functional Analysis

The topics of this volume are diverse, but all of them are related to a huge area in analysis and applications where remarkably deep results and original approaches of Professor Maz'ya play a fundamental role. World-recognized experts present their new results covering, in particular, the following topics: Beurling's minimum principle, inverse hyperbolic problems, degenerate oblique derivative problems, the Lp-dissipativity connected with the Lp-contractivity of the generated semigroups, optimal control of a biharmonic obstacle problem sharp bilateral bounds of Green's function for the...

Professor Maz'ya - one of the main developers of the modern theory of Sobolev spaces - contributed to the theory in many various directions. The strong influence of his fundamental works is traced in recent results presented in this volume from world-recognized specialists. The topics cover various aspects of the theory of function spaces, including Orlicz-Sobolev spaces, weighted Sobolev spaces, Dirichlet spaces, Besov Spaces with negative exponents, fractional Sobolev spaces on half-spaces and sharp constants in the Hardy inequality, Maz'ya's capacitary analogue of the co-area inequality...

This volume brings readers up to date on different aspects of operator theory and its applications, including mathematical physics, hydrodynamics, magnetohydrodynamics, quantum mechanics, astrophysics as well as the theory of networks and systems. Of practical use to a wide readership in pure and applied mathematics, physics and engineering sciences.

The Virasoro algebra is an infinite dimensional Lie algebra that plays an increasingly important role in mathematics and theoretical physics. This book describes some fundamental facts about the representation theory of the Virasoro algebra in a self-contained manner. Topics include the structure of Verma modules and Fock modules, the classification of (unitarizable) Harish-Chandra modules, tilting equivalence, and the rational vertex operator algebras associated to the so-called minimal series representations.

Covering a wide range of material, this book has three appendices which...

Almost Automorphic and Almost Periodic Functions in Abstract Spaces introduces and develops the theory of almost automorphic vector-valued functions in Bochner's sense and the study of almost periodic functions in a locally convex space in a homogenous and unified manner. It also applies the results obtained to study almost automorphic solutions of abstract differential equations, expanding the core topics with a plethora of groundbreaking new results and applications. For the sake of clarity, and to spare the reader unnecessary technical hurdles, the concepts are studied using...

This text offers a rigorous introduction into the theory and methods of convergence spaces and gives concrete applications to the problems of functional analysis. While there are a few books dealing with convergence spaces and a great many on functional analysis, there are none with this particular focus.

The book demonstrates the applicability of convergence structures to functional analysis. Highlighted here is the role of continuous convergence, a convergence structure particularly appropriate to function spaces. It is shown to provide an excellent dual structure for both topological...

In contrast to other books devoted to the averaging method and the method of integral manifolds, in the present book we study oscillation systems with many varying frequencies. In the process of evolution, systems of this type can pass from one resonance state into another. This fact considerably complicates the investigation of nonlinear oscillations.

In the present monograph, a new approach based on exact uniform estimates of oscillation integrals is proposed. On the basis of this approach, numerous completely new results on the justification of the averaging method and its...

This book provides an overview of the theory of p-adic (and more general non-Archimedean) dynamical systems. The main part of the book is devoted to discrete dynamical systems. It presents a model of probabilistic thinking on p-adic mental space based on ultrametric diffusion. Coverage also details p-adic neural networks and their applications to cognitive sciences: learning algorithms, memory recalling.