This accessible, undergraduate-level text illustrates the role of algebras of holomorphic functions in the solution of an important engineering problem: the stabilization of a linear control system. Its concise and self-contained treatment avoids the use of higher mathematics and forms a bridge to mo... read more
Methods of the Theory of Functions of Many Complex Variables by Vasiliy Sergeyevich Vladimirov This systematic exposition outlines fundamentals of the theory of single sheeted holomorphic domains and illustrates applications to quantum field theory, the theory of functions, and differential equations with constant coefficients. 1966 edition.
General Theory of Functions and Integration by Angus E. Taylor Uniting a variety of approaches to the study of integration, a well-known professor presents a single-volume "blend of the particular and the general, of the concrete and the abstract." 1966 edition.
Problem Book in the Theory of Functions by Konrad Knopp Single-volume edition of renowned collection of problems. Part 1 contains more than 300 problems dealing with fundamental concepts; part 2 has over 230 problems in advanced theory. Includes hints and full solutions to all problems.
Elements of the Theory of Functions and Functional Analysis by A. N. Kolmogorov, S. V. Fomin Advanced-level text, now available in a single volume, discusses metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque intervals, Hilbert space, more. Exercises. 1957 edition.
Theory of Functions, Parts I and II by Konrad Knopp Handy one-volume edition. Part I considers general foundations of theory of functions; Part II stresses special and characteristic functions. Proofs given in detail. Introduction. Bibliographies.
Partially Ordered Algebraic Systems by Laszlo Fuchs This monograph by a distinguished mathematician constitutes the first systematic summary of research concerning partially ordered groups, semigroups, rings, and fields. The high-level, self-contained treatment features numerous problems. 1963 edition.
This accessible, undergraduate-level text illustrates the role of algebras of holomorphic functions in the solution of an important engineering problem: the stabilization of a linear control system. Its concise and self-contained treatment avoids the use of higher mathematics and forms a bridge to more advanced treatments. The treatment consists of two components: the algebraic framework, which serves as the abstract language for posing and solving the problem of stabilization; and the analysis component, which examines properties of specific rings of holomorphic functions. Elementary, self-contained, and constructive proofs elucidate the explorations of rings of holomorphic functions relevant in control theory. Introductory chapters on control theory and stable transfer functions are followed by surveys of unstable plants and the stabilization problem and its solution. The text concludes with suggestions for further reading and a bibliography.
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