Functional Equations In A Single Variable (mathematics Monographs)
by Marek Kuczma /
1968 / English / DjVu
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This book is exclusively concerned with functional equations in which only one independent variable occurs. But the difference equations and recurrences are not included, although they belong to the same type. They may be regarded as independent subjects, which since 1860 have again and again been presented in book form (e.g. Norlund, T. Fort, Gelfond, Montel, Goldberg, H.Levy, Lessman, Meschkowski, to mention only the most important examples). A few exceptions from this principle are questions which are not usually found in books on differences, such as the problem of monotonic or convex solutions of difference equations, etc. It must be stressed, however, that, though difference equations are not separately discussed, many of the results contained in the present book apply also to difference equations. Of the various aspects of functional equations the author has chosen to present those which are most likely to form a foundation of a theory. Thus the main stress has been laid on questions of existence and uniqueness. The book is kept on an elementary level, and advanced methods have been avoided throughout. The use of fixed point theorems in function spaces is an exception but it is doubtful whether these methods can nowadays be regarded as advanced. Apart from this, no special knowledge is required from the reader, except the elements of the calculus and some basic facts from the theory of complex functions. Only the section on Riemann's Zeta function requires in addition the knowledge of Dirichlet series, but it may be omitted in reading without loss.
