The Bochner-Martinelli Integral and Its Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Bochner-Martinelli Integral and Its Applications write by Alexander M. Kytmanov. This book was released on 2012-12-06. The Bochner-Martinelli Integral and Its Applications available in PDF, EPUB and Kindle. 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.
Linear Functional Equations. Operator Approach
Linear Functional Equations. Operator Approach - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Linear Functional Equations. Operator Approach write by Anatolij Antonevich. This book was released on 2012-12-06. Linear Functional Equations. Operator Approach available in PDF, EPUB and Kindle. 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.
Topics in Several Complex Variables
Topics in Several Complex Variables - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topics in Several Complex Variables write by Zair Ibragimov. This book was released on 2016-04-21. Topics in Several Complex Variables available in PDF, EPUB and Kindle. This volume contains the proceedings of the Special Session on Several Complex Variables, which was held during the first USA-Uzbekistan Conference on Analysis and Mathematical Physics from May 20–23, 2014, at California State University, Fullerton. This volume covers a wide variety of topics in pluripotential theory, symplectic geometry and almost complex structures, integral formulas, holomorphic extension, and complex dynamics. In particular, the reader will find articles on Lagrangian submanifolds and rational convexity, multidimensional residues, S-parabolic Stein manifolds, Segre varieties, and the theory of quasianalytic functions.
Functional Analytic Methods In Complex Analysis And Applications To Partial Differential Equations
Functional Analytic Methods In Complex Analysis And Applications To Partial Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Functional Analytic Methods In Complex Analysis And Applications To Partial Differential Equations write by A S A Mshimba. This book was released on 1995-10-17. Functional Analytic Methods In Complex Analysis And Applications To Partial Differential Equations available in PDF, EPUB and Kindle. These proceedings concentrate on recent results in the following fields of complex analysis: complex methods for solving boundary value problems with piecewise smooth boundary data, complex methods for linear and nonlinear differential equations and systems of second order, and applications of scales of Banach spaces to initial value problems.Some problems in higher dimensions (such as the unification of global and local existence theorems for holomorphic functions and an elementary approach to Clifford analysis) are also discussed.Particular emphasis is placed on Symbolic Computation in Complex Analysis and on the new approaches to teach mathematical analysis based on interactions between complex analysis and partial differential equations.
Topics In Complex Analysis, Differential Geometry And Methematical Physics - Proceedings Of The Third International Workshop On Complex Structures And Vector Fields
Topics In Complex Analysis, Differential Geometry And Methematical Physics - Proceedings Of The Third International Workshop On Complex Structures And Vector Fields - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topics In Complex Analysis, Differential Geometry And Methematical Physics - Proceedings Of The Third International Workshop On Complex Structures And Vector Fields write by Stancho Dimiev. This book was released on 1997-07-01. Topics In Complex Analysis, Differential Geometry And Methematical Physics - Proceedings Of The Third International Workshop On Complex Structures And Vector Fields available in PDF, EPUB and Kindle. The Third International Workshop on Complex Structures and Vector Fields was held to exchange information on current topics in complex analysis, differential geometry and mathematical physics, and to find new subjects in these fields.This volume contains many interesting and important articles in complex analysis (including quaternionic analysis), functional analysis, topology, differential geometry (hermitian geometry, surface theory), and mathematical physics (quantum mechanics, hamilton mechanics).
