- Published Year: 2009
- Page count: 435
- File Size: 2 Mb
- Language: English
- Published by: Birkhäuser Basel
- Visited by: 7
- Rating/Review: 5.0
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ISBN:
3034601255
9783034601252
9783034601269
Keywords:
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Learn MoreHolomorphic Operator Functions of One Variable and Applications: Methods from Complex Analysis in Several Variables
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Each download or ask from book AI costs 2 points. To earn more free points, please visit the Points Guide Page and complete some valuable actions.Welcome to the comprehensive study of holomorphic operator functions as presented in the book, "Holomorphic Operator Functions of One Variable and Applications: Methods from Complex Analysis in Several Variables." Authored by Israel Gohberg and Jürgen Leiterer, this book is a profound exploration of the intersection between operator theory and complex analysis, showcasing methods and applications critical to understanding these mathematical disciplines.
Detailed Summary of the Book
The book embarks on a robust journey through the realm of holomorphic functions, beginning with foundational concepts before advancing to more intricate themes. By placing a pivotal emphasis on operator functions specifically of one variable, the authors fill a unique niche in mathematical literature. The text elaborates on holomorphic functions in the context of operator theory, extending well beyond the traditional approach to functional analysis.
The authors systematically introduce complex analysis techniques in several variables, underpinning the principles required to understand the behaviour and properties of operator functions. Readers are meticulously guided through the characterization of meromorphic and holomorphic operator functions, alongside valuable insights into the theoretical aspects and practical applications in solving complex linear equations.
Moreover, the book provides a rich collection of mathematical tools and methodologies that are essential for students and researchers dealing with boundary value problems, spectral theory, and system theory. Comprehensive examples and exercises underscore each chapter, facilitating a deeper understanding of the intricate relationships between operators and holomorphy in various dimensions. This structure ensures the book is not only academically rigorous but also accessible to a broad audience interested in advanced mathematics.
Key Takeaways
- Gain a thorough understanding of holomorphic operator functions and their applications in modern mathematical theory.
- Explore advanced concepts in complex analysis with a focus on operator theory, supported by practical examples and scholarly exercises.
- Learners will acquire the skills to apply complex analysis methods to multidimensional operator problems, expanding their mathematical toolkit significantly.
Famous Quotes from the Book
"Understanding the subtleties of holomorphic operator functions requires not just mathematical rigor, but a clear vision of their analytical power in higher dimensions."
"Each operator, when viewed through the lens of holomorphic functions, unveils a rich tapestry woven from threads of complex analysis."
Why This Book Matters
The significance of "Holomorphic Operator Functions of One Variable and Applications" lies in its groundbreaking synthesis of complex analysis and operator theory. For students, researchers, and professionals in mathematics and engineering disciplines, understanding these concepts opens new pathways for theoretical exploration and innovative problem-solving techniques. The book stands as a crucial resource for extending knowledge in mathematical sciences, aligning with cutting-edge research and practical demands in engineering and applied mathematics.
By equipping readers with a robust framework for analyzing complex operator functions, Gohberg and Leiterer invite exploration into fields of quantum mechanics, control theory, and mathematical physics, where comprehending operator behavior in complex domains is paramount. Emphasizing both theory and application ensures that this book remains a timeless asset in advancing mathematical comprehension and capability.
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