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Author: Herbert Amann Publisher: Springer Science & Business Media ISBN: 3764374802 Category : Mathematics Languages : en Pages : 468
Book Description
This third volume concludes our introduction to analysis, wherein we ?nish laying the groundwork needed for further study of the subject. As with the ?rst two, this volume contains more material than can treated in a single course. It is therefore important in preparing lectures to choose a suitable subset of its content; the remainder can be treated in seminars or left to independent study. For a quick overview of this content, consult the table of contents and the chapter introductions. Thisbookisalsosuitableasbackgroundforothercoursesorforselfstudy. We hope that its numerous glimpses into more advanced analysis will arouse curiosity and so invite students to further explore the beauty and scope of this branch of mathematics. In writing this volume, we counted on the invaluable help of friends, c- leagues, sta?, and students. Special thanks go to Georg Prokert, Pavol Quittner, Olivier Steiger, and Christoph Walker, who worked through the entire text cr- ically and so helped us remove errors and make substantial improvements. Our thanks also goes out to Carlheinz Kneisel and Bea Wollenmann, who likewise read the majority of the manuscript and pointed out various inconsistencies. Without the inestimable e?ortofour “typesetting perfectionist”, this volume could not have reached its present form: her tirelessness and patience with T X E and other software brought not only the end product, but also numerous previous versions,to a high degree of perfection. For this contribution, she has our greatest thanks.
Author: Herbert Amann Publisher: Springer Science & Business Media ISBN: 3764374802 Category : Mathematics Languages : en Pages : 468
Book Description
This third volume concludes our introduction to analysis, wherein we ?nish laying the groundwork needed for further study of the subject. As with the ?rst two, this volume contains more material than can treated in a single course. It is therefore important in preparing lectures to choose a suitable subset of its content; the remainder can be treated in seminars or left to independent study. For a quick overview of this content, consult the table of contents and the chapter introductions. Thisbookisalsosuitableasbackgroundforothercoursesorforselfstudy. We hope that its numerous glimpses into more advanced analysis will arouse curiosity and so invite students to further explore the beauty and scope of this branch of mathematics. In writing this volume, we counted on the invaluable help of friends, c- leagues, sta?, and students. Special thanks go to Georg Prokert, Pavol Quittner, Olivier Steiger, and Christoph Walker, who worked through the entire text cr- ically and so helped us remove errors and make substantial improvements. Our thanks also goes out to Carlheinz Kneisel and Bea Wollenmann, who likewise read the majority of the manuscript and pointed out various inconsistencies. Without the inestimable e?ortofour “typesetting perfectionist”, this volume could not have reached its present form: her tirelessness and patience with T X E and other software brought not only the end product, but also numerous previous versions,to a high degree of perfection. For this contribution, she has our greatest thanks.
Author: Herbert Amann Publisher: Springer Science & Business Media ISBN: 3764373237 Category : Mathematics Languages : en Pages : 426
Book Description
"This textbook provides an outstanding introduction to analysis. It is distinguished by its high level of presentation and its focus on the essential.'' (Zeitschrift für Analysis und ihre Anwendung 18, No. 4 - G. Berger, review of the first German edition) "One advantage of this presentation is that the power of the abstract concepts are convincingly demonstrated using concrete applications.'' (W. Grölz, review of the first German edition)
Author: Roger Godement Publisher: Springer ISBN: 3319160532 Category : Mathematics Languages : en Pages : 321
Book Description
Volume III sets out classical Cauchy theory. It is much more geared towards its innumerable applications than towards a more or less complete theory of analytic functions. Cauchy-type curvilinear integrals are then shown to generalize to any number of real variables (differential forms, Stokes-type formulas). The fundamentals of the theory of manifolds are then presented, mainly to provide the reader with a "canonical'' language and with some important theorems (change of variables in integration, differential equations). A final chapter shows how these theorems can be used to construct the compact Riemann surface of an algebraic function, a subject that is rarely addressed in the general literature though it only requires elementary techniques. Besides the Lebesgue integral, Volume IV will set out a piece of specialized mathematics towards which the entire content of the previous volumes will converge: Jacobi, Riemann, Dedekind series and infinite products, elliptic functions, classical theory of modular functions and its modern version using the structure of the Lie algebra of SL(2,R).
Author: S. M. Nikol'skii Publisher: Springer Science & Business Media ISBN: 3662099616 Category : Mathematics Languages : en Pages : 228
Book Description
In the Part at hand the authors undertake to give a presentation of the historical development of the theory of imbedding of function spaces, of the internal as well as the externals motives which have stimulated it, and of the current state of art in the field, in particular, what regards the methods employed today. The impossibility to cover all the enormous material connected with these questions inevitably forced on us the necessity to restrict ourselves to a limited circle of ideas which are both fundamental and of principal interest. Of course, such a choice had to some extent have a subjective character, being in the first place dictated by the personal interests of the authors. Thus, the Part does not constitute a survey of all contemporary questions in the theory of imbedding of function spaces. Therefore also the bibliographical references given do not pretend to be exhaustive; we only list works mentioned in the text, and a more complete bibliography can be found in appropriate other monographs. O.V. Besov, v.1. Burenkov, P.1. Lizorkin and V.G. Maz'ya have graciously read the Part in manuscript form. All their critical remarks, for which the authors hereby express their sincere thanks, were taken account of in the final editing of the manuscript.
Author: Kimberly F. Johnson Publisher: Springer Science & Business Media ISBN: 0306483548 Category : Science Languages : en Pages : 252
Book Description
As microarray technology has matured, data analysis methods have advanced as well. Methods Of Microarray Data Analysis III is the third book in this pioneering series dedicated to the existing new field of microarrays. While initial techniques focused on classification exercises (volume I of this series), and later on pattern extraction (volume II of this series), this volume focuses on data quality issues. Problems such as background noise determination, analysis of variance, and errors in data handling are highlighted. Three tutorial papers are presented to assist with a basic understanding of underlying principles in microarray data analysis, and twelve new papers are highlighted analyzing the same CAMDA'02 datasets: the Project Normal data set or the Affymetrix Latin Square data set. A comparative study of these analytical methodologies brings to light problems, solutions and new ideas. This book is an excellent reference for academic and industrial researchers who want to keep abreast of the state of art of microarray data analysis.
Author: Peter Warwick (Prof.) Publisher: Royal Society of Chemistry ISBN: 0854042636 Category : Science Languages : en Pages : 231
Book Description
The analysis of radionuclides in the environment became extremely important after the accident at Chernobyl in1986. The accident made scientists aware that accurate methods of radionuclide analyses are essential in order to estimate the risk to the public from released radioactivity. Methods are still being developed today because of the ongoing requirement to monitor environmental radioactivity and, to assess the radionuclide waste inventory for the recently proposed intermediate radioactive waste repository. This book brings together current developments in radioactive analyses. Environmenta.
Author: Tomas Dominguez Benavides Publisher: World Scientific ISBN: 9812818448 Category : Mathematics Languages : en Pages : 209
Book Description
This volume comprises a collection of articles by leading researchers in mathematical analysis. It provides the reader with an extensive overview of the present-day research in different areas of mathematical analysis (complex variable, harmonic analysis, real analysis and functional analysis) that holds great promise for current and future developments. These review articles are highly useful for those who want to learn about these topics, as many results scattered in the literature are reflected through the many separate papers featured herein.
Author: Terence Tao Publisher: Hindustan Book Agency and Indian National Science Academy ISBN: 9788185931944 Category : Mathematical analysis Languages : en Pages : 0
Book Description
Suitable for undergraduates who have already been exposed to calculus, this title includes material that starts at the very beginning - the construction of number systems and set theory, then goes on to the basics of analysis, through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral.
Author: Viktor Petrovich Khavin Publisher: Springer Science & Business Media ISBN: 9783540519980 Category : Mathematics Languages : en Pages : 340
Book Description
Classical harmonic analysis is an important part of modern physics and mathematics, comparable in its significance with calculus. Created in the 18th and 19th centuries as a distinct mathematical discipline it continued to develop, conquering new unexpected areas and producing impressive applications to a multitude of problems. It is widely understood that the explanation of this miraculous power stems from group theoretic ideas underlying practically everything in harmonic analysis. This book is an unusual combination of the general and abstract group theoretic approach with a wealth of very concrete topics attractive to everybody interested in mathematics. Mathematical literature on harmonic analysis abounds in books of more or less abstract or concrete kind, but the lucky combination as in this volume can hardly be found.
Author: Herbert Amann
Author: Herbert Amann
Author: Herbert Amann
Author: Roger Godement
Author: S. M. Nikol'skii
Author: Wieslawa J. Kaczor
Author: Kimberly F. Johnson
Author: Peter Warwick (Prof.)
Author: Tomas Dominguez Benavides
Author: Terence Tao
Author: Viktor Petrovich Khavin