Principles of Analysis Measure, Integration, Functional Analysis, and Applications
Auteur : Junghenn Hugo D.
Principles of Analysis: Measure, Integration, Functional Analysis, and Applications prepares readers for advanced courses in analysis, probability, harmonic analysis, and applied mathematics at the doctoral level. The book also helps them prepare for qualifying exams in real analysis. It is designed so that the reader or instructor may select topics suitable to their needs. The author presents the text in a clear and straightforward manner for the readers? benefit. At the same time, the text is a thorough and rigorous examination of the essentials of measure, integration and functional analysis.
The book includes a wide variety of detailed topics and serves as a valuable reference and as an efficient and streamlined examination of advanced real analysis. The text is divided into four distinct sections: Part I develops the general theory of Lebesgue integration; Part II is organized as a course in functional analysis; Part III discusses various advanced topics, building on material covered in the previous parts; Part IV includes two appendices with proofs of the change of the variable theorem and a joint continuity theorem. Additionally, the theory of metric spaces and of general topological spaces are covered in detail in a preliminary chapter .
Features:
- Contains direct and concise proofs with attention to detail
- Features a substantial variety of interesting and nontrivial examples
- Includes nearly 700 exercises ranging from routine to challenging with hints for the more difficult exercises
- Provides an eclectic set of special topics and applications
About the Author:
Hugo D. Junghenn is a professor of mathematics at The George Washington University. He has published numerous journal articles and is the author of several books, including Option Valuation: A First Course in Financial Mathematics and A Course in Real Analysis. His research interests include functional analysis, semigroups, and probability.
Measurable Sets. Measurable Functions. Integration. Further Topics in Measure Theory. Banach Spaces. Hilbert Spaces. Locally Convex Spaces. Banach Algebras. Harmonic Analysis on Locally Compact Groups. Probability Theory. Operator Theory. Appendices.
Hugo D. Junghenn is a professor of mathematics at The George Washington University. He has published numerous journal articles and is the author of several books, including Option Valuation: A First Course in Financial Mathematics and A Course in Real Analysis. His research interests include functional analysis, semigroups, and probability.
Date de parution : 01-2023
17.8x25.4 cm
Date de parution : 04-2018
17.8x25.4 cm
Thèmes de Principles of Analysis :
Mots-clés :
Locally Convex Spaces; Functional analysis; Locally Convex Space; Plancherel Theorem; Fubini’s Theorem; Measurable Spaces; Balanced Neighborhood; Neighborhood Base; TVS; Continuous Linear Functionals; Topologically Isomorphic; Schwartz Function; Commutative Banach Algebra; Inversion Theorem; Riemann Lebesgue Lemma; Quotient Topology; Dominated Convergence Theorem; Banach Algebra; Measurable Transformation; Lower Semicontinuous; Open Neighborhood; Vector Space; Real TVS; Continuous Linear Mapping; Measurable Functions; Relative Topology