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Author: I. N. Vekua
Publisher: Elsevier
ISBN: 1483184676
Category : Mathematics
Languages : en
Pages : 699
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Book Description
Generalized Analytic Functions is concerned with foundations of the general theory of generalized analytic functions and some applications to problems of differential geometry and theory of shells. Some classes of functions and operators are discussed, along with the reduction of a positive differential quadratic form to the canonical form. Boundary value problems and infinitesimal bendings of surfaces are also considered. Comprised of six chapters, this volume begins with a detailed treatment of various problems of the general theory of generalized analytic functions as as well as boundary value problems. The reader is introduced to some classes of functions and functional spaces, with emphasis on functions of two independent variables. Subsequent chapters focus on the problem of reducing a positive differential quadratic form to the canonical form; basic properties of solutions of elliptic systems of partial differential equations of the first order, in a two-dimensional domain; and some boundary value problems for an elliptic system of equations of the first order and for an elliptic equation of the second order, in a two-dimensional domain. The final part of the book deals with problems of the theory of surfaces and the membrane theory of shells. This book is intended for students of advanced courses of the mechanico-mathematical faculties, postgraduates, and research workers.
Author: I. N. Vekua
Publisher: Elsevier
ISBN: 1483184676
Category : Mathematics
Languages : en
Pages : 699
Get Book
Book Description
Generalized Analytic Functions is concerned with foundations of the general theory of generalized analytic functions and some applications to problems of differential geometry and theory of shells. Some classes of functions and operators are discussed, along with the reduction of a positive differential quadratic form to the canonical form. Boundary value problems and infinitesimal bendings of surfaces are also considered. Comprised of six chapters, this volume begins with a detailed treatment of various problems of the general theory of generalized analytic functions as as well as boundary value problems. The reader is introduced to some classes of functions and functional spaces, with emphasis on functions of two independent variables. Subsequent chapters focus on the problem of reducing a positive differential quadratic form to the canonical form; basic properties of solutions of elliptic systems of partial differential equations of the first order, in a two-dimensional domain; and some boundary value problems for an elliptic system of equations of the first order and for an elliptic equation of the second order, in a two-dimensional domain. The final part of the book deals with problems of the theory of surfaces and the membrane theory of shells. This book is intended for students of advanced courses of the mechanico-mathematical faculties, postgraduates, and research workers.
Author: Wolfgang Tutschke
Publisher: Springer Science & Business Media
ISBN: 3662099438
Category : Mathematics
Languages : en
Pages : 189
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Book Description
The purpose of the present book is to solve initial value problems in classes of generalized analytic functions as well as to explain the functional-analytic background material in detail. From the point of view of the theory of partial differential equations the book is intend ed to generalize the classicalCauchy-Kovalevskayatheorem, whereas the functional-analytic background connected with the method of successive approximations and the contraction-mapping principle leads to the con cept of so-called scales of Banach spaces: 1. The method of successive approximations allows to solve the initial value problem du CTf = f(t,u), (0. 1) u(O) = u , (0. 2) 0 where u = u(t) ist real o. r vector-valued. It is well-known that this method is also applicable if the function u belongs to a Banach space. A completely new situation arises if the right-hand side f(t,u) of the differential equation (0. 1) depends on a certain derivative Du of the sought function, i. e. , the differential equation (0,1) is replaced by the more general differential equation du dt = f(t,u,Du), (0. 3) There are diff. erential equations of type (0. 3) with smooth right-hand sides not possessing any solution to say nothing about the solvability of the initial value problem (0,3), (0,2), Assume, for instance, that the unknown function denoted by w is complex-valued and depends not only on the real variable t that can be interpreted as time but also on spacelike variables x and y, Then the differential equation (0.
Author: Il'ia Nestorovič forme avant 2007 Vekua
Publisher:
ISBN:
Category :
Languages : en
Pages : 668
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Book Description
Author: William T. Ross
Publisher: American Mathematical Soc.
ISBN: 0821831755
Category : Mathematics
Languages : en
Pages : 165
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Book Description
The theory of generalized analytic continuation studies continuations of meromorphic functions in situations where traditional theory says there is a natural boundary. This broader theory touches on a remarkable array of topics in classical analysis, as described in the book. The authors use the strong analogy with the summability of divergent series to motivate the subject. They are careful to cover the various types of continuations, attempting to unify them and suggesting some open questions. The book also addresses the role of such continuations in approximation theory and operator theory. The introductory overview provides a useful look at the history and context of the theory.
Author: Ilʹâ Nestorovič Vekua
Publisher:
ISBN: 9781483168869
Category :
Languages : en
Pages :
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Book Description
Author:
Publisher:
ISBN:
Category : Analytic functions
Languages : en
Pages : 668
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Book Description
Author: N K Bliev
Publisher: CRC Press
ISBN: 9780582288614
Category : Mathematics
Languages : en
Pages : 160
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Book Description
This book studies the foundations of the general theory of generalized analytic functions in fractional spaces. The employment of fractional spaces and embedding theorems support applications of the theory of generalized analytic functions. The results obtained are applicable to the theory of singular integral equations, boundary value problems for elliptic differential equations, functions of a complex variable, as well as the theory of plates and shells. The book will be of interest to scientific workers and specialists interested in these questions and likewise to advanced students in mechanical engineering faculties.
Author: Yuri L. Rodin
Publisher: Springer
ISBN: 3540480188
Category : Mathematics
Languages : en
Pages : 134
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Book Description
Author: Helmut Florian
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 350
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Book Description
Contains papers from a January 1997 conference at the Technical University of Graz. Part I looks at generalized analytic functions, dealing not only with problems in the complex plane but also related problems in higher dimensions where several complex variables and Clifford Analysis are used. Part II is devoted to applications of partial differential equations to mechanics, with contributions on boundary elements and asymptotic methods, and hemivariational inequalities. A substantial number of papers in Part II deal with problems of ocean acoustics. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Author: V. S. Vladimirov
Publisher: CRC Press
ISBN: 9780415273565
Category : Mathematics
Languages : en
Pages : 332
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Book Description
This volume presents the general theory of generalized functions, including the Fourier, Laplace, Mellin, Hilbert, Cauchy-Bochner and Poisson integral transforms and operational calculus, with the traditional material augmented by the theory of Fourier series, abelian theorems, and boundary values of helomorphic functions for one and several variables. The author addresses several facets in depth, including convolution theory, convolution algebras and convolution equations in them, homogenous generalized functions, and multiplication of generalized functions. This book will meet the needs of researchers, engineers, and students of applied mathematics, control theory, and the engineering sciences.
