Kategoria BISAC: Mathematics >> Functional Analysis

This monograph systematically develops and considers the so-called "dressing method" for solving differential equations (both linear and nonlinear), a means to generate new non-trivial solutions for a given equation from the (perhaps trivial) solution of the same or related equation. Throughout, the text exploits the "linear experience" of presentation, with special attention given to the algebraic aspects of the main mathematical constructions and to practical rules of obtaining new solutions.

This monograph explores nonoscillation and existence of positive solutions for functional differential equations and describes their applications to maximum principles, boundary value problems and stability of these equations. In view of this objective the volume considers a wide class of equations including, scalar equations and systems of different types, equations with variable types of delays and equations with variable deviations of the argument. Each chapter includes an introduction and preliminaries, thus making it complete. Appendices at the end of the book cover reference...

In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, "Ramanujan's lost notebook." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony.

This volume is the third of five volumes that the authors plan to write on Ramanujan's lost notebook and other manuscripts and fragments found...

"Hypernumbers and Extrafunctions" presents a rigorous mathematical approach to operate with infinite values. First, concepts of real and complex numbers are expanded to include a new universe of numbers called hypernumbers which includes infinite quantities. This brief extends classical calculus based on real functions by introducing extrafunctions, which generalize not only the concept of a conventional function but also the concept of a distribution. Extrafucntions have been also efficiently used for a rigorous mathematical definition of the Feynman path integral, as well as for...

This monograph is an introduction to some special aspects of topology, functional analysis, and analysis for the advanced reader. It also wants to develop a degree theory for function triples which unifies and extends most known degree theories. The book aims to be self-contained and many chapters could even serve as a basis of a course on the covered topics. Only knowledge in basic calculus and of linear algebra is assumed.

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...

New results, presented from world-recognized experts, are close to scientific interests of Professor Maz'ya and use, directly or indirectly, the fundamental influential Maz'ya's works penetrating, in a sense, the theory of PDEs. In particular, the following topics are covered: semilinear elliptic equations with exponential monlinearity, stationary Navier-Stokes equations on Lipschitz domains in Riemannian manifolds, Stokes equations in a thin cylindrical elastic tube the Neumann problem for 4th order linear partial differential operators the Stokes system in convex polyhedra, periodic...