Complex Analysis and Spectral Theory PDF Download

Author: Nikolaĭ Kapitonovich Nikolʹskiĭ
Publisher:
ISBN:
Category : Functions of complex variables
Languages : en
Pages : 480

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Book Description

Author: V. P. Havin
Publisher:
ISBN: 9783662213513
Category :
Languages : en
Pages : 492

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Book Description

Author: V. P. Havin
Publisher: Springer
ISBN: 3540386262
Category : Mathematics
Languages : en
Pages : 491

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Book Description

Author: H. Garth Dales
Publisher: American Mathematical Soc.
ISBN: 1470446928
Category : Education
Languages : en
Pages : 280

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Book Description
This volume contains the proceedings of the Conference on Complex Analysis and Spectral Theory, in celebration of Thomas Ransford's 60th birthday, held from May 21–25, 2018, at Laval University, Québec, Canada. Spectral theory is the branch of mathematics devoted to the study of matrices and their eigenvalues, as well as their infinite-dimensional counterparts, linear operators and their spectra. Spectral theory is ubiquitous in science and engineering because so many physical phenomena, being essentially linear in nature, can be modelled using linear operators. On the other hand, complex analysis is the calculus of functions of a complex variable. They are widely used in mathematics, physics, and in engineering. Both topics are related to numerous other domains in mathematics as well as other branches of science and engineering. The list includes, but is not restricted to, analytical mechanics, physics, astronomy (celestial mechanics), geology (weather modeling), chemistry (reaction rates), biology, population modeling, economics (stock trends, interest rates and the market equilibrium price changes). There are many other connections, and in recent years there has been a tremendous amount of work on reproducing kernel Hilbert spaces of analytic functions, on the operators acting on them, as well as on applications in physics and engineering, which arise from pure topics like interpolation and sampling. Many of these connections are discussed in articles included in this book.

Author:
Publisher: Elsevier
ISBN: 0080871151
Category : Mathematics
Languages : en
Pages : 106

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Spectral Theory and Complex Analysis

Author: Jurgen Poschel
Publisher: Academic Press
ISBN: 0080874495
Category : Mathematics
Languages : en
Pages : 209

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Inverse Spectral Theory

Author: Vladimir Müller
Publisher: Springer Science & Business Media
ISBN: 3764382651
Category : Mathematics
Languages : en
Pages : 444

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Book Description
This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. Many results appear here for the first time in a monograph.

Author: Pietro Aiena
Publisher: Springer Science & Business Media
ISBN: 1402025254
Category : Mathematics
Languages : en
Pages : 452

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A signi?cant sector of the development of spectral theory outside the classical area of Hilbert space may be found amongst at multipliers de?ned on a complex commutative Banach algebra A. Although the general theory of multipliers for abstract Banach algebras has been widely investigated by several authors, it is surprising how rarely various aspects of the spectral theory, for instance Fredholm theory and Riesz theory, of these important classes of operators have been studied. This scarce consideration is even more surprising when one observes that the various aspects of spectral t- ory mentioned above are quite similar to those of a normal operator de?ned on a complex Hilbert space. In the last ten years the knowledge of the spectral properties of multip- ers of Banach algebras has increased considerably, thanks to the researches undertaken by many people working in local spectral theory and Fredholm theory. This research activity recently culminated with the publication of the book of Laursen and Neumann [214], which collects almost every thing that is known about the spectral theory of multipliers.

Author: Harold G. Dales
Publisher:
ISBN: 9781470454531
Category : Analytic functions
Languages : en
Pages :

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Book Description

Author: David Borthwick
Publisher: Springer Nature
ISBN: 3030380025
Category : Mathematics
Languages : en
Pages : 339

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Book Description
This textbook offers a concise introduction to spectral theory, designed for newcomers to functional analysis. Curating the content carefully, the author builds to a proof of the spectral theorem in the early part of the book. Subsequent chapters illustrate a variety of application areas, exploring key examples in detail. Readers looking to delve further into specialized topics will find ample references to classic and recent literature. Beginning with a brief introduction to functional analysis, the text focuses on unbounded operators and separable Hilbert spaces as the essential tools needed for the subsequent theory. A thorough discussion of the concepts of spectrum and resolvent follows, leading to a complete proof of the spectral theorem for unbounded self-adjoint operators. Applications of spectral theory to differential operators comprise the remaining four chapters. These chapters introduce the Dirichlet Laplacian operator, Schrödinger operators, operators on graphs, and the spectral theory of Riemannian manifolds. Spectral Theory offers a uniquely accessible introduction to ideas that invite further study in any number of different directions. A background in real and complex analysis is assumed; the author presents the requisite tools from functional analysis within the text. This introductory treatment would suit a functional analysis course intended as a pathway to linear PDE theory. Independent later chapters allow for flexibility in selecting applications to suit specific interests within a one-semester course.