Integral Representation and the Computation of Combinatorial Sums PDF Download
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Author: G. P. Egorychev
Publisher: American Mathematical Soc.
ISBN: 9780821898093
Category : Mathematics
Languages : en
Pages : 302
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Book Description
This monograph should be of interest to a broad spectrum of readers: specialists in discrete and continuous mathematics, physicists, engineers, and others interested in computing sums and applying complex analysis in discrete mathematics. It contains investigations on the problem of finding integral representations for and computing finite and infinite sums (generating functions); these arise in practice in combinatorial analysis, the theory of algorithms and programming on a computer, probability theory, group theory, and function theory, as well as in physics and other areas of knowledge. A general approach is presented for computing sums and other expressions in closed form by reducing them to one-dimensional and multiple integrals, most often to contour integrals.
Author: G. P. Egorychev
Publisher: American Mathematical Soc.
ISBN: 9780821898093
Category : Mathematics
Languages : en
Pages : 302
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Book Description
This monograph should be of interest to a broad spectrum of readers: specialists in discrete and continuous mathematics, physicists, engineers, and others interested in computing sums and applying complex analysis in discrete mathematics. It contains investigations on the problem of finding integral representations for and computing finite and infinite sums (generating functions); these arise in practice in combinatorial analysis, the theory of algorithms and programming on a computer, probability theory, group theory, and function theory, as well as in physics and other areas of knowledge. A general approach is presented for computing sums and other expressions in closed form by reducing them to one-dimensional and multiple integrals, most often to contour integrals.
Author: R. Michael Range
Publisher: Springer Science & Business Media
ISBN: 1475719183
Category : Mathematics
Languages : en
Pages : 405
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Book Description
The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex convexity" related to the remarkable extension properties of holomorphic functions in more than one variable. It then continues with a comprehensive introduction to integral representations, and concludes with complete proofs of substantial global results on domains of holomorphy and on strictly pseudoconvex domains inC", including, for example, C. Fefferman's famous Mapping Theorem. The most important new feature of this book is the systematic inclusion of many of the developments of the last 20 years which centered around integral representations and estimates for the Cauchy-Riemann equations. In particu lar, integral representations are the principal tool used to develop the global theory, in contrast to many earlier books on the subject which involved methods from commutative algebra and sheaf theory, and/or partial differ ential equations. I believe that this approach offers several advantages: (1) it uses the several variable version of tools familiar to the analyst in one complex variable, and therefore helps to bridge the often perceived gap between com plex analysis in one and in several variables; (2) it leads quite directly to deep global results without introducing a lot of new machinery; and (3) concrete integral representations lend themselves to estimations, therefore opening the door to applications not accessible by the earlier methods.
Author: Jaroslav Lukeš
Publisher: Walter de Gruyter
ISBN: 3110203200
Category : Mathematics
Languages : en
Pages : 732
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Book Description
This monograph presents the state of the art of convexity, with an emphasis to integral representation. The exposition is focused on Choquet's theory of function spaces with a link to compact convex sets. An important feature of the book is an interplay between various mathematical subjects, such as functional analysis, measure theory, descriptive set theory, Banach spaces theory and potential theory. A substantial part of the material is of fairly recent origin and many results appear in the book form for the first time. The text is self-contained and covers a wide range of applications. From the contents: Geometry of convex sets Choquet theory of function spaces Affine functions on compact convex sets Perfect classes of functions and representation of affine functions Simplicial function spaces Choquet's theory of function cones Topologies on boundaries Several results on function spaces and compact convex sets Continuous and measurable selectors Construction of function spaces Function spaces in potential theory and Dirichlet problem Applications
Author: I. Reiner
Publisher: Springer
ISBN: 3540350071
Category : Mathematics
Languages : en
Pages : 284
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Book Description
Author: Walter Roth
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3111315479
Category : Mathematics
Languages : en
Pages : 266
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Book Description
This book presents a wide-ranging approach to operator-valued measures and integrals of both vector-valued and set-valued functions. It covers convergence theorems and an integral representation for linear operators on spaces of continuous vector-valued functions on a locally compact space. These are used to extend Choquet theory, which was originally formulated for linear functionals on spaces of real-valued functions, to operators of this type.
Author: Luiz C. L. Botelho
Publisher: Nova Publishers
ISBN: 9781594540196
Category : Mathematics
Languages : en
Pages : 384
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Book Description
The special Internet categories are: Physics; Engineering Quantum Physics; and Applied Mathematics. The emphasis in this monograph is on non-trivial path integral variable change on previously obtained path integral solutions for difficult stochastic and functional equations by keeping the main objective to arrive at...another path integral which the author expects to be in a 'final' suitable form of become predictive. Note that path-integrals are mathematical objects specially tailored to the work of our modern 'slavers': computer machines.
Author: Daniel Zwillinger
Publisher: Elsevier
ISBN: 0080471110
Category : Mathematics
Languages : en
Pages : 1220
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Book Description
The Table of Integrals, Series, and Products is the essential reference for integrals in the English language. Mathematicians, scientists, and engineers, rely on it when identifying and subsequently solving extremely complex problems. Since publication of the first English-language edition in 1965, it has been thoroughly revised and enlarged on a regular basis, with substantial additions and, where necessary, existing entries corrected or revised. The seventh edition includes a fully searchable CD-Rom.- Fully searchable CD that puts information at your fingertips included with text- Most up to date listing of integrals, series andproducts - Provides accuracy and efficiency in work
Author: Lev Abramovich Aĭzenberg
Publisher: American Mathematical Soc.
ISBN: 0821815504
Category : Mathematics
Languages : en
Pages : 296
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Book Description
This book deals with integral representations of holomorphic functions of several complex variables, the multidimensional logarithmic residue, and the theory of multidimensional residues. Applications are given to implicit function theory, systems of nonlinear equations, computation of the multiplicity of a zero of a mapping, and computation of combinatorial sums in closed form. Certain applications in multidimensional complex analysis are considered. The monograph is intended for specialists in theoretical and applied mathematics and theoretical physics, and for postgraduate and graduate students interested in multidimensional complex analysis or its applications.
Author: John Voight
Publisher: Springer Nature
ISBN: 3030566943
Category : Mathematics
Languages : en
Pages : 877
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Book Description
This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.
Author: Alexander M. Kytmanov
Publisher: Springer
ISBN: 3319216597
Category : Mathematics
Languages : en
Pages : 236
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Book Description
The monograph is devoted to integral representations for holomorphic functions in several complex variables, such as Bochner-Martinelli, Cauchy-Fantappiè, Koppelman, multidimensional logarithmic residue etc., and their boundary properties. The applications considered are problems of analytic continuation of functions from the boundary of a bounded domain in C^n. In contrast to the well-known Hartogs-Bochner theorem, this book investigates functions with the one-dimensional property of holomorphic extension along complex lines, and includes the problems of receiving multidimensional boundary analogs of the Morera theorem. This book is a valuable resource for specialists in complex analysis, theoretical physics, as well as graduate and postgraduate students with an understanding of standard university courses in complex, real and functional analysis, as well as algebra and geometry.
