This textbook in point set topology is aimed at an upper-undergraduate audience. Its gentle pace will be useful to students who are still learning to write proofs. Prerequisites include calculus and at least one semester of analysis, where the student has been properly exposed to the ideas of basic set theory such as subsets, unions, intersections, and functions, as well as convergence and other topological notions in the real line. Appendices are included to bridge the gap between this new material and material found in an analysis course. Metric spaces are one of the more prevalent topological spaces used in other areas and are therefore introduced in the first chapter and emphasized throughout the text. This also conforms to the approach of the book to start with the particular and work toward the more general. Chapter 2 defines and develops abstract topological spaces, with metric spaces as the source of inspiration, and with a focus on Hausdorff spaces. The final chapter concentrates on continuous real-valued functions, culminating in a development of paracompact spaces.
This book presents a basic introduction to complex analysis in both an interesting and a rigorous manner. It contains enough material for a full year's course, and the choice of material treated is reasonably standard and should be satisfactory for most first courses in complex analysis. The approach to each topic appears to be carefully thought out both as to mathematical treatment and pedagogical presentation, and the end result is a very satisfactory book." --MATHSCINET
This book covers topics appropriate for a first-year graduate course preparing students for the doctorate degree. The first half of the book presents the core of measure theory, including an introduction to the Fourier transform. This material can easily be covered in a semester. The second half of the book treats basic functional analysis and can also be covered in a semester. After the basics, it discusses linear transformations, duality, the elements of Banach algebras, and C*-algebras. It concludes with a characterization of the unitary equivalence classes of normal operators on a Hilbert space. The book is self-contained and only relies on a background in functions of a single variable and the elements of metric spaces. Following the author's belief that the best way to learn is to start with the particular and proceed to the more general, it contains numerous examples and exercises.
This book is an introductory text in functional analysis. Unlike many modern treatments, it begins with the particular and works its way to the more general. From the reviews: "This book is an excellent text for a first graduate course in functional analysis....Many interesting and important applications are included....It includes an abundance of exercises, and is written in the engaging and lucid style which we have come to expect from the author." --MATHEMATICAL REVIEWS
Let S be a subnormal operator on a Hilbert space [script]H with minimal normal extension [italic]N operating on [italic]K, and let [lowercase Greek]Mu be a scalar valued spectral measure for [italic]N. If [italic]P[infinity symbol]([lowercase Greek]Mu) denotes the weak star closure of the polynomials in [italic]L[infinity symbol]([lowercase Greek]Mu) = [italic]L1[infinity symbol]([lowercase Greek]Mu) then for [script]f in [italic]P[infinity symbol]([lowercase Greek]Mu) it follows that [script]f([italic]N) leaves [script]H invariant; if [script]f([italic]S) is defined as the restriction of [script]f([italic]N) to [script]H then a functional calculus for [italic]S is obtained. This functional calculus is investigated in this paper.
This book presents a basic introduction to complex analysis in both an interesting and a rigorous manner. It contains enough material for a full year's course, and the choice of material treated is reasonably standard and should be satisfactory for most first courses in complex analysis. The approach to each topic appears to be carefully thought out both as to mathematical treatment and pedagogical presentation, and the end result is a very satisfactory book." --MATHSCINET
This book discusses a variety of problems which are usually treated in a second course on the theory of functions of one complex variable, the level being gauged for graduate students. It treats several topics in geometric function theory as well as potential theory in the plane, covering in particular: conformal equivalence for simply connected regions, conformal equivalence for finitely connected regions, analytic covering maps, de Branges' proof of the Bieberbach conjecture, harmonic functions, Hardy spaces on the disk, potential theory in the plane. A knowledge of integration theory and functional analysis is assumed.
This textbook in point set topology is aimed at an upper-undergraduate audience. Its gentle pace will be useful to students who are still learning to write proofs. Prerequisites include calculus and at least one semester of analysis, where the student has been properly exposed to the ideas of basic set theory such as subsets, unions, intersections, and functions, as well as convergence and other topological notions in the real line. Appendices are included to bridge the gap between this new material and material found in an analysis course. Metric spaces are one of the more prevalent topological spaces used in other areas and are therefore introduced in the first chapter and emphasized throughout the text. This also conforms to the approach of the book to start with the particular and work toward the more general. Chapter 2 defines and develops abstract topological spaces, with metric spaces as the source of inspiration, and with a focus on Hausdorff spaces. The final chapter concentrates on continuous real-valued functions, culminating in a development of paracompact spaces.
This book illustrates connections between various courses taken by undergraduate mathematics majors. As such it can be used as a text for a capstone course. The chapters are essentially independent, and the instructor can choose the topics that will form the course and thus tailor the syllabus to suit the backgrounds and abilities of the students. At the end of such a course the graduating seniors should glimpse mathematics not as a series of independent courses but as something more like an integrated body of knowledge. The book has numerous exercises and examples so that the student has many opportunities to see the material illustrated and fleshed out.
In a certain sense, subnormal operators were introduced too soon because the theory of function algebras and rational approximation was also in its infancy and could not be properly used to examine the class of operators. The progress in the last several years grew out of applying the results of rational approximation." from the Preface. This book is the successor to the author's 1981 book on the same subject. In addition to reflecting the great strides in the development of subnormal operator theory since the first book, the present work is oriented towards rational functions rather than polynomials. Although the book is a research monograph, it has many of the traits of a textbook including exercises. The book requires background in function theory and functional analysis, but is otherwise fairly self-contained. The first few chapters cover the basics about subnormal operator theory and present a study of analytic functions on the unit disk. Other topics included are: some results on hypernormal operators, an exposition of rational approximation interspersed with applications to operator theory, a study of weak-star rational approximation, a set of results that can be termed structure theorems for subnormal operators, and a proof that analytic bounded point evaluations exist.
This book covers topics appropriate for a first-year graduate course preparing students for the doctorate degree. The first half of the book presents the core of measure theory, including an introduction to the Fourier transform. This material can easily be covered in a semester. The second half of the book treats basic functional analysis and can also be covered in a semester. After the basics, it discusses linear transformations, duality, the elements of Banach algebras, and C*-algebras. It concludes with a characterization of the unitary equivalence classes of normal operators on a Hilbert space. The book is self-contained and only relies on a background in functions of a single variable and the elements of metric spaces. Following the author's belief that the best way to learn is to start with the particular and proceed to the more general, it contains numerous examples and exercises.
Professor Ripley, in this 1980 study of Julius Caesar, offers one of the most detailed stage histories ever attempted, focusing upon aspects both of English and American staging from 1599 to 1973. His primary sources include promptbooks and groundplans, letters, diaries and reviews. He approaches the play from four different angles: he examines the texts used in all major productions, and makes valuable deductions about the taste and sensibility of an age from cuts, alterations, additions and redistribution of parts. He explains in detail the staging of the play at various points in time, and demonstrates how sets and costumes, bits of business, handling of crowd scenes and lighting affected its business. He reconstructs performances of the four main roles by the greater and lesser lights of each period. Finally, he comments on the way in which the theories of critics and, in modern times, directors' ideas have influenced understanding of the play.
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