Описание: The purpose of this book is to provide a careful and accessible account along modern lines of the subject which the title deals, as well as to discuss problems of current interest in the field. More precisely this book is devoted to the functional-analytic approach to a class of degenerate boundary value problems for second-order elliptic integro-differential operators which includes as particular cases the Dirichlet and Robin problems. This class of boundary value problems provides a new example of analytic semigroups. As an application, we construct a strong Markov process corresponding to such a diffusion phenomenon that a Markovian particle moves both by jumps and continuously in the state space until it dies at the time when it reaches the set where the particle is definitely absorbed.
Описание: Lists the required preliminary knowledge in set and measure theory, topology and algebra. This book gives details on solutions of the Cauchy equation and of the Jensen inequality, in particular on continuous convex functions, Hamel bases, and on inequalities following from the Jensen inequality.
Автор: Shoikhet D. Название: Semigroups in Geometrical Function Theory ISBN: 0792371119 ISBN-13(EAN): 9780792371113 Издательство: Springer Рейтинг: Цена: 10449 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Functional Equations, Inequalities and Applications provides an extensive study of several important equations and inequalities, useful in a number of problems in mathematical analysis. Subjects dealt with include the generalized Cauchy functional equation, the Ulam stability theory in the geometry of partial differential equations, stability of a quadratic functional equation in Banach modules, functional equations and mean value theorems, isometric mappings, functional inequalities of iterative type, related to a Cauchy functional equation, the median principle for inequalities and applications, Hadamard and Dragomir-Agarwal inequalities, the Euler formulae and convex functions and approximate algebra homomorphisms. Also included are applications to some problems of pure and applied mathematics.This book will be of particular interest to mathematicians and graduate students whose work involves functional equations, inequalities and applications.
Автор: Forte Название: Functional Equations and Inequalities ISBN: 3642110029 ISBN-13(EAN): 9783642110023 Издательство: Springer Рейтинг: Цена: 4697 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: J. Acz?l: Some applications of functional equations and inequalities to information measures.- J.A. Baker: Functional equations in vector space, part II.- I Fenyo: Sur les ?quations distributionnelles.- B. Forte: Applications of functional equations and inequalities to information theory.- S. Golab: Sur l’?quation fonctionnelle des brigade.- E. Hille: Mean-values and functional equations.- J. Kamp? de Feriet: Applications of functional equations and inequalities to information theory. Measure of information by a set of observers: a functional equation.- M. Kuczma: Convex functions.- S. Kurepa: Functional equations on vector spaces.- E. Lukacs: Inequalities and functional equations in probability theory.- M.A. McKiernan: Difference and mean-value type functional equations.- T.S. Motzkin: Solutions of differential and functional inequalities.- C.T. Ng: Uniqueness theorems in the theory of functional equations and related homotopy.- A.M. Ostrowski: Integral inequalities.- H. Schwerdtfeger: Remark on an inequality for monotonic functions.
Описание: "Functional Equations and Inequalities with Applications" presents a comprehensive, nearly encyclopedic, study of the classical topic of functional equations.
Nowadays, the field of functional equations is an ever-growing branch of mathematics with far-reaching applications; it is increasingly used to investigate problems in mathematical
analysis, combinatorics, biology, information theory, statistics, physics, the behavioral sciences, and engineering. This self-contained monograph explores all aspects of functional
equations and their applications to related topics, such as differential equations, integral equations, the Laplace transformation, the calculus of finite differences, and many other basic
tools in analysis.
Each chapter examines a particular family of equations and gives an in-depth study of its applications; examples and exercises to support the material. The
book is intended as a reference tool for any student, professional (researcher), or mathematician studying in a field where functional equations can be applied. It can also be used as a
primary text in a classroom setting or for self-study.
Finally, it could be an inspiring entree into an active area of mathematical exploration for engineers and other scientists
who would benefit from this careful, rigorous exposition.
Описание: This volume covers the topic in functional equations in a broad sense and is written by authors who are in this field for the past 50 years. It contains the basic notions of functional equations, the methods of solving functional equations, the growth of functional equations in the last four decades and an extensive reference list on fundamental research papers that investigate the stability results of different types of functional equations and functional inequalities. This volume starts by taking the reader from the fundamental ideas to higher levels of results that appear in recent research papers. Its step-by-step expositions are easy for the reader to understand and admire the elegant results and findings on the stability of functional equations. remove
Автор: Arveson William Название: Noncommutative Dynamics and E-Semigroups ISBN: 0387001514 ISBN-13(EAN): 9780387001517 Издательство: Springer Рейтинг: Цена: 15674 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book introduces the notion of an E-semigroup, a generalization of the known concept of E_O-semigroup. These objects are families of endomorphisms of a von Neumann algebra satisfying certain natural algebraic and continuity conditions. Its thorough approach is ideal for graduate students and research mathematicians.
Описание: With emphasis on positive semigroups on Banach lattices and perturbation techniques, this book is an introduction to semigroup theory. It presents a survey of the results and also provides worked examples to help absorb the theoretical material. It then deals with the application of the developed theory to a variety of problems.
Автор: Engel Название: A Short Course on Operator Semigroups ISBN: 0387313419 ISBN-13(EAN): 9780387313412 Издательство: Springer Рейтинг: Цена: 8359 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The book offers a direct and up-to-date introduction to the theory of one-parameter semigroups of linear operators on Banach spaces. It contains the fundamental results of the theory such as the Hille-Yoshida generation theorem, the bounded perturbation theorem, and the Trotter-Kato approximation theorem, but also treats the spectral theory of semigroups and its consequences for the qualitative behavior.The book is intended for students and researchers who want to become acquainted with the concept of semigroups in order to work with it in fields like partial and functional differential equations, stochastic processes, infinite dimensional control theory, or dynamical systems coming from physics or biology.
Описание: Nonlinear semigroup theory is not only of intrinsic interest, but is also important in the study of evolution problems. In the last forty years, the generation theory of
flows of holomorphic mappings has been of great interest in the theory of Markov stochastic branching processes, the theory of composition operators, control theory, and optimization.
It transpires that the asymptotic behavior of solutions to evolution equations is applicable to the study of the geometry of certain domains in complex spaces.
provided with a systematic overview of many results concerning both nonlinear semigroups in metric and Banach spaces and the fixed point theory of mappings, which are
nonexpansive with respect to hyperbolic metrics (in particular, holomorphic self-mappings of domains in Banach spaces). The exposition is organized in a readable and intuitive manner,
presenting basic functional and complex analysis as well as very recent developments.
Описание: Since the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become a necessary discipline in functional analysis and differential equations. This book presents that theory and its basic applications.
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