Regularity Properties of Functional Equations in Several Variables
Title | Regularity Properties of Functional Equations in Several Variables PDF eBook |
Author | Antal Járai |
Publisher | Springer Science & Business Media |
Pages | 367 |
Release | 2006-03-30 |
Genre | Mathematics |
ISBN | 038724414X |
This book illustrates the basic ideas of regularity properties of functional equations by simple examples. It then treats most of the modern results about regularity of non-composite functional equations of several variables in a unified fashion. A long introduction highlights the basic ideas for beginners and several applications are also included.
Regularity Properties of Functional Equations in Several Variables
Title | Regularity Properties of Functional Equations in Several Variables PDF eBook |
Author | Antal Járai |
Publisher | Springer |
Pages | 0 |
Release | 2008-11-01 |
Genre | Mathematics |
ISBN | 9780387505077 |
This book illustrates the basic ideas of regularity properties of functional equations by simple examples. It then treats most of the modern results about regularity of non-composite functional equations of several variables in a unified fashion. A long introduction highlights the basic ideas for beginners and several applications are also included.
Regularity Properties of Functional Equations
Title | Regularity Properties of Functional Equations PDF eBook |
Author | Antal Járai |
Publisher | |
Pages | 77 |
Release | 1996 |
Genre | |
ISBN |
Introduction to Functional Equations
Title | Introduction to Functional Equations PDF eBook |
Author | Costas Efthimiou |
Publisher | American Mathematical Soc. |
Pages | 381 |
Release | 2011-10-13 |
Genre | Mathematics |
ISBN | 0821853147 |
Functions and their properties have been part of the rigorous precollege curriculum for decades. And functional equations have been a favorite topic of the leading national and international mathematical competitions. Yet the subject has not received equal attention by authors at an introductory level. The majority of the books on the topic remain unreachable to the curious and intelligent precollege student. The present book is an attempt to eliminate this disparity. The book opens with a review chapter on functions, which collects the relevant foundational information on functions, plus some material potentially new to the reader. The next chapter presents a working definition of functional equations and explains the difficulties in trying to systematize the theory. With each new chapter, the author presents methods for the solution of a particular group of equations. Each chapter is complemented with many solved examples, the majority of which are taken from mathematical competitions and professional journals. The book ends with a chapter of unsolved problems and some other auxiliary material. The book is an invaluable resource for precollege and college students who want to deepen their knowledge of functions and their properties, for teachers and instructors who wish to enrich their curricula, and for any lover of mathematical problem-solving techniques. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
Introduction to Functional Equations
Title | Introduction to Functional Equations PDF eBook |
Author | Prasanna K. Sahoo |
Publisher | CRC Press |
Pages | 465 |
Release | 2011-02-08 |
Genre | Mathematics |
ISBN | 1439841160 |
Introduction to Functional Equations grew out of a set of class notes from an introductory graduate level course at the University of Louisville. This introductory text communicates an elementary exposition of valued functional equations where the unknown functions take on real or complex values. In order to make the presentation as manageable as p
Linear Functional Equations. Operator Approach
Title | Linear Functional Equations. Operator Approach PDF eBook |
Author | Anatolij Antonevich |
Publisher | Birkhäuser |
Pages | 188 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 3034889771 |
In this book we shall study linear functional equations of the form m bu(x) == Lak(X)U(Qk(X)) = f(x), (1) k=l where U is an unknown function from a given space F(X) of functions on a set X, Qk: X -+ X are given mappings, ak and f are given functions. Our approach is based on the investigation of the operators given by the left-hand side of equa tion (1). In what follows such operators will be called functional operators. We will pay special attention to the spectral properties of functional operators, first of all, to invertibility and the Noether property. Since the set X, the space F(X), the mappings Qk and the coefficients ak are arbitrary, the class of operators of the form (1) is very rich and some of its individ ual representatives are related with problems arising in various areas of mathemat ics and its applications. In addition to the classical theory of functional equations, among such areas one can indicate the theory of functional-differential equations with deviating argument, the theory of nonlocal problems for partial differential equations, the theory of boundary value problems for the equation of a vibrating string and equations of mixed type, a number of problems of the general theory of operator algebras and the theory of dynamical systems, the spectral theory of au tomorphisms of Banach algebras, and other problems.
Functional Equations on Groups
Title | Functional Equations on Groups PDF eBook |
Author | Henrik Stetkr |
Publisher | World Scientific |
Pages | 395 |
Release | 2013 |
Genre | Mathematics |
ISBN | 981451313X |
This volume provides an accessible and coherent introduction to some of the scientific progress on functional equations on groups in the last two decades. It presents the latest methods of treating the topic and contains new and transparent proofs. Its scope extends from the classical functional equations on the real line to those on groups, in particular, non-abelian groups. This volume presents, in careful detail, a number of illustrative examples like the cosine equation on the Heisenberg group and on the group SL(2, R). Some of the examples are not even seen in existing monographs. Thus, it is an essential source of reference for further investigations.