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| Author | : Leon Ehrenpreis |
| Publisher | : Courier Corporation |
| Total Pages | : 532 |
| Release | : 2011-11-30 |
| Genre | : Mathematics |
| ISBN | : 0486153037 |
Suitable for advanced undergraduates and graduate students, this text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations. 1970 edition.
| Author | : Leon Ehrenpreis |
| Publisher | : |
| Total Pages | : 530 |
| Release | : 1970 |
| Genre | : Fourier transformations |
| ISBN | : 9780608123516 |
This text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations. It begins by establishing the quotient structure theorem or fundamental principle of Fourier analysis, and then focuses on applications to partial differential equations. The final section explores functions and their role in Fourier representation. Problems. 1970 edtion.
| Author | : Leon Ehrenpreis |
| Publisher | : |
| Total Pages | : 506 |
| Release | : 1970 |
| Genre | : |
| ISBN | : |
| Author | : Steven G. Krantz |
| Publisher | : CRC Press |
| Total Pages | : 351 |
| Release | : 2019-04-16 |
| Genre | : Mathematics |
| ISBN | : 1000000354 |
The idea of complex numbers dates back at least 300 years—to Gauss and Euler, among others. Today complex analysis is a central part of modern analytical thinking. It is used in engineering, physics, mathematics, astrophysics, and many other fields. It provides powerful tools for doing mathematical analysis, and often yields pleasing and unanticipated answers. This book makes the subject of complex analysis accessible to a broad audience. The complex numbers are a somewhat mysterious number system that seems to come out of the blue. It is important for students to see that this is really a very concrete set of objects that has very concrete and meaningful applications. Features: This new edition is a substantial rewrite, focusing on the accessibility, applied, and visual aspect of complex analysis This book has an exceptionally large number of examples and a large number of figures. The topic is presented as a natural outgrowth of the calculus. It is not a new language, or a new way of thinking. Incisive applications appear throughout the book. Partial differential equations are used as a unifying theme.
| Author | : Pierre Lelong |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 283 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642703445 |
I - Entire functions of several complex variables constitute an important and original chapter in complex analysis. The study is often motivated by certain applications to specific problems in other areas of mathematics: partial differential equations via the Fourier-Laplace transformation and convolution operators, analytic number theory and problems of transcen dence, or approximation theory, just to name a few. What is important for these applications is to find solutions which satisfy certain growth conditions. The specific problem defines inherently a growth scale, and one seeks a solution of the problem which satisfies certain growth conditions on this scale, and sometimes solutions of minimal asymp totic growth or optimal solutions in some sense. For one complex variable the study of solutions with growth conditions forms the core of the classical theory of entire functions and, historically, the relationship between the number of zeros of an entire function f(z) of one complex variable and the growth of If I (or equivalently log If I) was the first example of a systematic study of growth conditions in a general setting. Problems with growth conditions on the solutions demand much more precise information than existence theorems. The correspondence between two scales of growth can be interpreted often as a correspondence between families of bounded sets in certain Frechet spaces. However, for applications it is of utmost importance to develop precise and explicit representations of the solutions.
| Author | : Steven G. Krantz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 367 |
| Release | : 2009-05-24 |
| Genre | : Mathematics |
| ISBN | : 0817646698 |
This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.
| Author | : John P. D'Angelo |
| Publisher | : Springer |
| Total Pages | : 229 |
| Release | : 2019-05-24 |
| Genre | : Mathematics |
| ISBN | : 3030165140 |
This textbook provides a coherent, integrated look at various topics from undergraduate analysis. It begins with Fourier series, continues with Hilbert spaces, discusses the Fourier transform on the real line, and then turns to the heart of the book, geometric considerations. This chapter includes complex differential forms, geometric inequalities from one and several complex variables, and includes some of the author's original results. The concept of orthogonality weaves the material into a coherent whole. This textbook will be a useful resource for upper-undergraduate students who intend to continue with mathematics, graduate students interested in analysis, and researchers interested in some basic aspects of Cauchy-Riemann (CR) geometry. The inclusion of several hundred exercises makes this book suitable for a capstone undergraduate Honors class. This second edition contains a significant amount of new material, including a new chapter dedicated to the CR geometry of the unit sphere. This chapter builds upon the first edition by presenting recent results about groups associated with CR sphere maps. From reviews of the first edition: The present book developed from the teaching experiences of the author in several honors courses. .... All the topics are motivated very nicely, and there are many exercises, which make the book ideal for a first-year graduate course on the subject. .... The style is concise, always very neat, and proofs are given with full details. Hence, I certainly suggest this nice textbook to anyone interested in the subject, even for self-study. Fabio Nicola, Politecnico di Torino, Mathematical Reviews D’Angelo has written an eminently readable book, including excellent explanations of pretty nasty stuff for even the more gifted upper division players .... It certainly succeeds in hooking the present browser: I like this book a great deal. Michael Berg, Loyola Marymount University, Mathematical Association of America
| Author | : Steven G. Krantz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 301 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461215889 |
This book is written to be a convenient reference for the working scientist, student, or engineer who needs to know and use basic concepts in complex analysis. It is not a book of mathematical theory. It is instead a book of mathematical practice. All the basic ideas of complex analysis, as well as many typical applica tions, are treated. Since we are not developing theory and proofs, we have not been obliged to conform to a strict logical ordering of topics. Instead, topics have been organized for ease of reference, so that cognate topics appear in one place. Required background for reading the text is minimal: a good ground ing in (real variable) calculus will suffice. However, the reader who gets maximum utility from the book will be that reader who has had a course in complex analysis at some time in his life. This book is a handy com pendium of all basic facts about complex variable theory. But it is not a textbook, and a person would be hard put to endeavor to learn the subject by reading this book.
| Author | : Luogeng Hua |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 192 |
| Release | : 1963-12-31 |
| Genre | : Mathematics |
| ISBN | : 0821815563 |
| Author | : John P. D'Angelo |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 211 |
| Release | : 2013-09-24 |
| Genre | : Mathematics |
| ISBN | : 1461485266 |
Hermitian Analysis: From Fourier Series to Cauchy-Riemann Geometry provides a coherent, integrated look at various topics from undergraduate analysis. It begins with Fourier series, continues with Hilbert spaces, discusses the Fourier transform on the real line, and then turns to the heart of the book, geometric considerations. This chapter includes complex differential forms, geometric inequalities from one and several complex variables, and includes some of the author's results. The concept of orthogonality weaves the material into a coherent whole. This textbook will be a useful resource for upper-undergraduate students who intend to continue with mathematics, graduate students interested in analysis, and researchers interested in some basic aspects of CR Geometry. The inclusion of several hundred exercises makes this book suitable for a capstone undergraduate Honors class.
