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Author: Szolem Mandelbrojt
Publisher:
ISBN:
Category : Analytic functions
Languages : en
Pages : 740
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Book Description
Author: Szolem Mandelbrojt
Publisher:
ISBN:
Category : Analytic functions
Languages : en
Pages : 740
Get Book Here
Book Description
Author: Szolem Mandelbrojt
Publisher:
ISBN: 9781258632205
Category :
Languages : en
Pages : 150
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Book Description
Includes Classes Of Infinitely Differentiable Functions; And Some Aspects Of The Theory Of Analytic Functions Of A Complex Variable.
Author: Michael R. Mitchell
Publisher:
ISBN:
Category : Analytic functions
Languages : en
Pages : 20
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Book Description
Contents: Infinitely-differentiable and analytic functions; Entire solutions of the heat equation; A class of infinitely-differentiable non-analytic functions; and An infinitely-differentiable non-analytic solution.
Author: Steven G. Krantz
Publisher: Springer Science & Business Media
ISBN: 9780817642648
Category : Mathematics
Languages : en
Pages : 260
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Book Description
Key topics in the theory of real analytic functions are covered in this text,and are rather difficult to pry out of the mathematics literature.; This expanded and updated 2nd ed. will be published out of Boston in Birkhäuser Adavaned Texts series.; Many historical remarks, examples, references and an excellent index should encourage the reader study this valuable and exciting theory.; Superior advanced textbook or monograph for a graduate course or seminars on real analytic functions.; New to the second edition a revised and comprehensive treatment of the Faá de Bruno formula, topologies on the space of real analytic functions,; alternative characterizations of real analytic functions, surjectivity of partial differential operators, And the Weierstrass preparation theorem.
Author: Nikolai A. Shirokov
Publisher: Springer
ISBN: 3540391754
Category : Mathematics
Languages : en
Pages : 214
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Book Description
This research monograph concerns the Nevanlinna factorization of analytic functions smooth, in a sense, up to the boundary. The peculiar properties of such a factorization are investigated for the most common classes of Lipschitz-like analytic functions. The book sets out to create a satisfactory factorization theory as exists for Hardy classes. The reader will find, among other things, the theorem on smoothness for the outer part of a function, the generalization of the theorem of V.P. Havin and F.A. Shamoyan also known in the mathematical lore as the unpublished Carleson-Jacobs theorem, the complete description of the zero-set of analytic functions continuous up to the boundary, generalizing the classical Carleson-Beurling theorem, and the structure of closed ideals in the new wide range of Banach algebras of analytic functions. The first three chapters assume the reader has taken a standard course on one complex variable; the fourth chapter requires supplementary papers cited there. The monograph addresses both final year students and doctoral students beginning to work in this area, and researchers who will find here new results, proofs and methods.
Author: G. V. Badalyan
Publisher: American Mathematical Soc.
ISBN: 9780821898031
Category :
Languages : en
Pages : 204
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Book Description
A certain class of functions $C$ on an interval is called quasianalytic if any function in $C$ is uniquely determined by the values of its derivatives at any point. The obvious question, then, is how to reconstruct such a function from the sequence of values of its derivatives at a certain point. In order to answer that question, Badalyan combines a study of expanding functions in generalized factorial series with a study of quasipower series. The theory of quasipower series and its application to the reconstruction problem are explained in detail in this research monograph. Along the way other, related problems are solved, such as Borel's hypothesis that no quasianalytic function can have all positive derivatives at a point. While the treatment is technical, the theory is developed chapter by chapter in detail, and the first chapter is of an introductory nature. The quasipower series technique explained here provides the means to extend the previously known results and elucidates their nature in the most relevant manner. This method also allows for thorough investigation of numerous problems of the theory of functions of quasianalytic classes by graduate students and research mathematicians.
Author: Brian S. Thomson
Publisher: ClassicalRealAnalysis.com
ISBN: 143484367X
Category : Mathematics
Languages : en
Pages : 685
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Book Description
This is the second edition of the text Elementary Real Analysis originally published by Prentice Hall (Pearson) in 2001.Chapter 1. Real NumbersChapter 2. SequencesChapter 3. Infinite sumsChapter 4. Sets of real numbersChapter 5. Continuous functionsChapter 6. More on continuous functions and setsChapter 7. Differentiation Chapter 8. The IntegralChapter 9. Sequences and series of functionsChapter 10. Power seriesChapter 11. Euclidean Space R^nChapter 12. Differentiation on R^nChapter 13. Metric Spaces
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: I. M. Gel'fand
Publisher: Academic Press
ISBN: 1483262324
Category : Mathematics
Languages : en
Pages : 233
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Book Description
Generalized Functions, Volume 3: Theory of Differential Equations focuses on the application of generalized functions to problems of the theory of partial differential equations. This book discusses the problems of determining uniqueness and correctness classes for solutions of the Cauchy problem for systems with constant coefficients and eigenfunction expansions for self-adjoint differential operators. The topics covered include the bounded operators in spaces of type W, Cauchy problem in a topological vector space, and theorem of the Phragmén-Lindelöf type. The correctness classes for the Cauchy problem, systems that are Petrovski?-correct, and generalized eigenfunctions of self-adjoint operators are also reviewed. This text likewise covers the differentiation of functionals of strongly and weakly bounded variation. This volume is beneficial to students and researchers interested in the theory of differential equations.
Author: A. I. Markushevich
Publisher: American Mathematical Soc.
ISBN: 082183780X
Category : Analytic functions
Languages : en
Pages : 1178
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Book Description
