Orr Moshe Shalit – författare

Written as a textbook, A First Course in Functional Analysis is an introduction to basic functional analysis and operator theory, with an emphasis on Hilbert space methods. The aim of this book is to introduce the basic notions of functional analysis and operator theory without requiring the student to have taken a course in measure theory as a prerequisite. It is written and structured the way a course would be designed, with an emphasis on clarity and logical development alongside real applications in analysis. The background required for a student taking this course is minimal; basic linear algebra, calculus up to Riemann integration, and some acquaintance with topological and metric spaces.

The Analyst’s Gambit: A Second Course in Functional Analysis is a textbook written to serve a graduate course in Functional Analysis. It provides a sequel to the author’s previous volume, A First Course in Functional Analysis, but it is not necessary to have read one in order to make use of the other. As a graduate text, the reader is assumed to have taken undergraduate courses in set theory, calculus, metric spaces and topology, complex analysis, measure theory (or, alternatively, have enough mathematical maturity to carry on without having seen every particular fact that is used).A particular strength of the book is that it includes numerous applications. Besides being engaging and interesting in their own right, these applications also illustrate how functional analysis is used in other parts of mathematics. The applications to problems from varied fields (PDEs, Fourier series, group theory, neural networks, topology, etc.) constitute an enticing external motivation for studying functional analysis. There are also applications of the material to functional analytic problems (Lomonosov’s invariant subspace theorem, the spectral theorem, Stone’s theorem), showcasing the power of the results as well as the elegance and unity of the theory.Features• Can be used as the primary textbook for a graduate course in functional analysis• Rich variety of exercises• Emphasis on substantial and modern applicationsOrr Moshe Shalit is a professor of mathematics at the Technion Israel Institute of Technology, where he teaches and conducts research in operator theory, operator algebras, functional analysis and function theory. His first book, A First Course in Functional Analysis, was published by Chapman & Hall / CRC in 2017.

The Analyst’s Gambit: A Second Course in Functional Analysis is a textbook written to serve a graduate course in Functional Analysis. It provides a sequel to the author’s previous volume, A First Course in Functional Analysis, but it is not necessary to have read one in order to make use of the other. As a graduate text, the reader is assumed to have taken undergraduate courses in set theory, calculus, metric spaces and topology, complex analysis, measure theory (or, alternatively, have enough mathematical maturity to carry on without having seen every particular fact that is used).A particular strength of the book is that it includes numerous applications. Besides being engaging and interesting in their own right, these applications also illustrate how functional analysis is used in other parts of mathematics. The applications to problems from varied fields (PDEs, Fourier series, group theory, neural networks, topology, etc.) constitute an enticing external motivation for studying functional analysis. There are also applications of the material to functional analytic problems (Lomonosov’s invariant subspace theorem, the spectral theorem, Stone’s theorem), showcasing the power of the results as well as the elegance and unity of the theory.Features• Can be used as the primary textbook for a graduate course in functional analysis• Rich variety of exercises• Emphasis on substantial and modern applicationsOrr Moshe Shalit is a professor of mathematics at the Technion Israel Institute of Technology, where he teaches and conducts research in operator theory, operator algebras, functional analysis and function theory. His first book, A First Course in Functional Analysis, was published by Chapman & Hall / CRC in 2017.