Multidimensional Integral Representations
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Multidimensional Integral Representations
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Author : Alexander M. Kytmanov
language : en
Publisher: Springer
Release Date : 2015-09-09
Multidimensional Integral Representations written by Alexander M. Kytmanov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-09 with Mathematics categories.
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.
Integral Representations And Residues In Multidimensional Complex Analysis
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Author : Lev Abramovich Aĭzenberg
language : en
Publisher: American Mathematical Soc.
Release Date : 1983
Integral Representations And Residues In Multidimensional Complex Analysis written by Lev Abramovich Aĭzenberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
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.
The Bochner Martinelli Integral And Its Applications
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Author : Alexander M. Kytmanov
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
The Bochner Martinelli Integral And Its Applications written by Alexander M. Kytmanov and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The Bochner-Martinelli integral representation for holomorphic functions or'sev eral complex variables (which has already become classical) appeared in the works of Martinelli and Bochner at the beginning of the 1940's. It was the first essen tially multidimensional representation in which the integration takes place over the whole boundary of the domain. This integral representation has a universal 1 kernel (not depending on the form of the domain), like the Cauchy kernel in e . However, in en when n > 1, the Bochner-Martinelli kernel is harmonic, but not holomorphic. For a long time, this circumstance prevented the wide application of the Bochner-Martinelli integral in multidimensional complex analysis. Martinelli and Bochner used their representation to prove the theorem of Hartogs (Osgood Brown) on removability of compact singularities of holomorphic functions in en when n > 1. In the 1950's and 1960's, only isolated works appeared that studied the boundary behavior of Bochner-Martinelli (type) integrals by analogy with Cauchy (type) integrals. This study was based on the Bochner-Martinelli integral being the sum of a double-layer potential and the tangential derivative of a single-layer potential. Therefore the Bochner-Martinelli integral has a jump that agrees with the integrand, but it behaves like the Cauchy integral under approach to the boundary, that is, somewhat worse than the double-layer potential. Thus, the Bochner-Martinelli integral combines properties of the Cauchy integral and the double-layer potential.
Integral Representation And The Computation Of Combinatorial Sums
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Author : G. P. Egorychev
language : en
Publisher: American Mathematical Soc.
Release Date : 1984-12-31
Integral Representation And The Computation Of Combinatorial Sums written by G. P. Egorychev and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-12-31 with Mathematics categories.
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.
The Double Mellin Barnes Type Integrals And Their Applications To Convolution Theory
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Author : Thanh Hai Nguyen
language : en
Publisher: World Scientific
Release Date : 1992
The Double Mellin Barnes Type Integrals And Their Applications To Convolution Theory written by Thanh Hai Nguyen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
This book presents new results in the theory of the double Mellin-Barnes integrals popularly known as the general H-function of two variables.A general integral convolution is constructed by the authors and it contains Laplace convolution as a particular case and possesses a factorization property for one-dimensional H-transform. Many examples of convolutions for classical integral transforms are obtained and they can be applied for the evaluation of series and integrals.
The Double Mellin Barnes Type Integrals And Their Application To Convolution Theory
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Author : Semyon B Yakubovich
language : en
Publisher: World Scientific
Release Date : 1992-05-26
The Double Mellin Barnes Type Integrals And Their Application To Convolution Theory written by Semyon B Yakubovich and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-05-26 with Mathematics categories.
This book presents new results in the theory of the double Mellin-Barnes integrals popularly known as the general H-function of two variables.A general integral convolution is constructed by the authors and it contains Laplace convolution as a particular case and possesses a factorization property for one-dimensional H-transform. Many examples of convolutions for classical integral transforms are obtained and they can be applied for the evaluation of series and integrals.
Multidimensional Systems Theory And Applications
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Author : N.K. Bose
language : en
Publisher: Springer
Release Date : 2013-12-20
Multidimensional Systems Theory And Applications written by N.K. Bose and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-20 with Technology & Engineering categories.
Preface to Second Edition From the time that the original edition was published in 1985, multidimensional systems theory has matured into a discipline of research and teaching with an expanding array of applications. The international journal on Multidimensional Systems and Signal Processing, founded in 1990, is now in its fourteenth year. A biannual international workshop on n-D systems was launched in 1998 and the impressive number of special sessions, mini-symposia, monographs and special issues that have emerged bear testimony to the growing popularity and importance of the subject -matter among scientists in various disciplines including engineering, computer science, geophysics and mathematics. This second edition builds on the fundamentals expounded in the original book with the addition of important developments in theory as well as practice since 1985. Particular attention has been given to the consolidation of basic results, uni fication of theory and the diversification of applications. Chapters that remain have been reordered and updated in content and references. Some chapters, considered to be somewhat outdated, have been replaced with newer proven as well as poten tially significant results, inspired by some groundbreaking research and directions which are likely to stimulate further research. In addition to the description of some challenging open problems, posed in 1985, which have since been solved, new problems yet to be tackled are also included.
Path Integrals On Group Manifolds Representation Independent Propagators For General Lie Groups
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Author : Wolfgang Tome
language : en
Publisher: World Scientific
Release Date : 1998-03-31
Path Integrals On Group Manifolds Representation Independent Propagators For General Lie Groups written by Wolfgang Tome and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-03-31 with Science categories.
The quantization of physical systems moving on group and symmetric spaces has been an area of active research over the past three decades. This book shows that it is possible to introduce a representation-independent propagator for a real, separable, connected and simply connected Lie group with irreducible, square-integrable representations. For a given set of kinematical variables this propagator is a single generalized function independent of any particular choice of fiducial vector and the irreducible representations of the Lie group generated by these kinematical variables, which nonetheless correctly propagates each element of a continuous representation based on the coherent states associated with these kinematical variables.Furthermore, the book shows that it is possible to construct regularized lattice phase space path integrals for a real, separable, connected and simply connected Lie group with irreducible, square-integrable representations, and although the configuration space is in general a multidimensional curved manifold, it is shown that the resulting lattice phase space path integral has the form of a lattice phase space path integral on a multidimensional flat manifold. Hence, a novel and extremely natural phase space path integral quantization is obtained for general physical systems whose kinematical variables are the generators of a connected and simply connected Lie group. This novel phase space path integral quantization is (a) exact, (b) more general than, and (c) free from the limitations of the previously considered path integral quantizations of free physical systems moving on group manifolds.To illustrate the general theory, a representation-independent propagator is explicitly constructed for SU(2) and the affine group.
Multidimensional Residue Theory And Applications
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Author : Alekos Vidras
language : en
Publisher: American Mathematical Society
Release Date : 2023-10-18
Multidimensional Residue Theory And Applications written by Alekos Vidras and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-18 with Mathematics categories.
Residue theory is an active area of complex analysis with connections and applications to fields as diverse as partial differential and integral equations, computer algebra, arithmetic or diophantine geometry, and mathematical physics. Multidimensional Residue Theory and Applications defines and studies multidimensional residues via analytic continuation for holomorphic bundle-valued current maps. This point of view offers versatility and flexibility to the tools and constructions proposed, allowing these residues to be defined and studied outside the classical case of complete intersection. The book goes on to show how these residues are algebraic in nature, and how they relate and apply to a wide range of situations, most notably to membership problems, such as the Briançon–Skoda theorem and Hilbert's Nullstellensatz, to arithmetic intersection theory and to tropical geometry. This book will supersede the existing literature in this area, which dates back more than three decades. It will be appreciated by mathematicians and graduate students in multivariate complex analysis. But thanks to the gentle treatment of the one-dimensional case in Chapter 1 and the rich background material in the appendices, it may also be read by specialists in arithmetic, diophantine, or tropical geometry, as well as in mathematical physics or computer algebra.
Functional Integration And Semiclassical Expansions
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Author : Flor Langouche
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Functional Integration And Semiclassical Expansions written by Flor Langouche and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
This book is intended as a fairly complete presentation of what··'We call the discretization approach to functional integrals, i.e. path integrals defined as limits of discretized expressions. In its main parts it is based 0n the original work of the authors. We hope to have provided the readers with a rather complete and up-to-date bibliography, and we apologize to authors whose work has not been cited through ignorance ori our part. Our main concern has been to present a formalism that is practical and which can be adapted to make computations in the numerous areas where path integrals are being increasingly used. For these reasons applications, illustrative examples, and detailed calculations are included. The book is partially based on lectures given by one of us (E.T.) at the Institut de Physique Theorique of the u.c.L. (Louvain-la-Neuve). We thank Dr. M.E. Brachet (University of Paris) for his help in the redaction of chapter 8. We are indebted to many of our colleagues and especially to the members of the Instituut voor Theoretische Fysica, K.U. Leuven for their interest and encouragement. We also thank Professor Claudio Anguita, Dean of the Faculty of Physics and Mathematics of .the University of Chile, for his constant support. Special thanks are due to Christine Detroije and Lutgarde Dubois for their very fine and hard work in typing the manuscript.