Primer on Hilbert Space Operators

The book covers various topics in the theory of operators on Hilbert spaces, such as functional calculus, spectral theorems, compact operators, trace class and Hilbert-Schmidt operators, self-adjoint extensions, and one-parameter groups, using a novel tool called the z-transform to simplify the analysis of unbounded operators.

\n Format: Paperback / softback
\n Length: 200 pages
\n Publication date: 17 September 2018
\n Publisher: Birkhauser Verlag AG
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The book offers a comprehensive and concise introduction to the theory of operators on Hilbert spaces, covering a wide range of essential topics. It delves into the realm of functional calculus and spectral theorems, exploring the mathematical foundations of operator analysis. The text also discusses compact operators, trace class and Hilbert-Schmidt operators, self-adjoint extensions of symmetric operators, and one-parameter groups of operators.

One of the notable features of the book is its innovative approach to the exposition of unbounded operators. Instead of relying on traditional methods, the author employs a novel tool called the z-transform, which enables the encoding of full information about unbounded operators within bounded ones. This approach simplifies many technical aspects of the theory, making it more accessible to a broader audience.

Throughout the text, the author employs clear and concise explanations, accompanied by numerous examples and exercises, to aid in understanding and applying the theoretical concepts. The book is well-organized, with each chapter serving as a standalone unit, allowing readers to focus on specific topics as needed. Additionally, a comprehensive bibliography provides further resources for those interested in exploring the theory of operators in greater depth.

Whether you are a student pursuing a degree in mathematics, a researcher in the field of operator theory, or simply someone with an interest in mathematical analysis, this book is an invaluable resource. It provides a solid foundation in the theory of operators on Hilbert spaces, enabling you to advance your understanding of this important area of mathematics.

In conclusion, the book offers a comprehensive and accessible introduction to the theory of operators on Hilbert spaces, covering a wide range of topics and employing innovative techniques to simplify complex concepts. It is an essential resource for students, researchers, and anyone interested in mathematical analysis.

\n Weight: 340g\n
Dimension: 156 x 232 x 17 (mm)\n
ISBN-13: 9783319920603\n
Edition number: 1st ed. 2018\n