Introduction to the Theory of Linear Nonselfadjoint Operators PDF Download
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Author: Israel Gohberg
Publisher: American Mathematical Soc.
ISBN: 9780821886502
Category : Mathematics
Languages : en
Pages : 402
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Book Description
Author: Israel Gohberg
Publisher: American Mathematical Soc.
ISBN: 9780821886502
Category : Mathematics
Languages : en
Pages : 402
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Book Description
Author: Jonathan R. Partington
Publisher: Cambridge University Press
ISBN: 0521366119
Category : Mathematics
Languages : en
Pages : 113
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Book Description
Hankel operators are of wide application in mathematics and engineering and this account of them is both elementary and rigorous.
Author: Tailen Hsing
Publisher: John Wiley & Sons
ISBN: 0470016914
Category : Mathematics
Languages : en
Pages : 363
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Book Description
Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA). The self–contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self–adjoint and non self–adjoint operators. The probabilistic foundation for FDA is described from the perspective of random elements in Hilbert spaces as well as from the viewpoint of continuous time stochastic processes. Nonparametric estimation approaches including kernel and regularized smoothing are also introduced. These tools are then used to investigate the properties of estimators for the mean element, covariance operators, principal components, regression function and canonical correlations. A general treatment of canonical correlations in Hilbert spaces naturally leads to FDA formulations of factor analysis, regression, MANOVA and discriminant analysis. This book will provide a valuable reference for statisticians and other researchers interested in developing or understanding the mathematical aspects of FDA. It is also suitable for a graduate level special topics course.
Author: Fabio Bagarello
Publisher: John Wiley & Sons
ISBN: 1118855272
Category : Science
Languages : en
Pages : 432
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Book Description
A unique discussion of mathematical methods with applications to quantum mechanics Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects presents various mathematical constructions influenced by quantum mechanics and emphasizes the spectral theory of non-adjoint operators. Featuring coverage of functional analysis and algebraic methods in contemporary quantum physics, the book discusses the recent emergence of unboundedness of metric operators, which is a serious issue in the study of parity-time-symmetric quantum mechanics. The book also answers mathematical questions that are currently the subject of rigorous analysis with potentially significant physical consequences. In addition to prompting a discussion on the role of mathematical methods in the contemporary development of quantum physics, the book features: Chapter contributions written by well-known mathematical physicists who clarify numerous misunderstandings and misnomers while shedding light on new approaches in this growing area An overview of recent inventions and advances in understanding functional analytic and algebraic methods for non-selfadjoint operators as well as the use of Krein space theory and perturbation theory Rigorous support of the progress in theoretical physics of non-Hermitian systems in addition to mathematically justified applications in various domains of physics such as nuclear and particle physics and condensed matter physics An ideal reference, Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects is useful for researchers, professionals, and academics in applied mathematics and theoretical and/or applied physics who would like to expand their knowledge of classical applications of quantum tools to address problems in their research. Also a useful resource for recent and related trends, the book is appropriate as a graduate-level and/or PhD-level text for courses on quantum mechanics and mathematical models in physics.
Author: Ole H. Hald
Publisher: American Mathematical Soc.
ISBN: 0821804863
Category : Mathematics
Languages : en
Pages : 162
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Book Description
In this paper we consider an eigenvalue problem which arises in the study of rectangular membranes. The mathematical model is an elliptic equation, in potential form, with Dirichlet boundary conditions. We show that the potential is uniquely determined, up to an additive constant, by a subset of the nodal lines of the eigenfunctions. A formula is shown which, when the additive constant is given, yields an approximation to the potential at a dense set of points. We present an estimate for the error made by the formula. A substantial part of this work is the derivation of the asymptotic forms for a rich set of eigenvalues and eigenfunctions for a large set of rectangles.
Author: Alexander G. Ramm
Publisher: Springer Science & Business Media
ISBN: 9400945442
Category : Mathematics
Languages : en
Pages : 439
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Book Description
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Author: Luigi Accardi
Publisher: Springer Nature
ISBN: 3031061705
Category : Mathematics
Languages : en
Pages : 369
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Book Description
This proceedings volume gathers selected, peer-reviewed papers presented at the 41st International Conference on Infinite Dimensional Analysis, Quantum Probability and Related Topics (QP41) that was virtually held at the United Arab Emirates University (UAEU) in Al Ain, Abu Dhabi, from March 28th to April 1st, 2021. The works cover recent developments in quantum probability and infinite dimensional analysis, with a special focus on applications to mathematical physics and quantum information theory. Covered topics include white noise theory, quantum field theory, quantum Markov processes, free probability, interacting Fock spaces, and more. By emphasizing the interconnection and interdependence of such research topics and their real-life applications, this reputed conference has set itself as a distinguished forum to communicate and discuss new findings in truly relevant aspects of theoretical and applied mathematics, notably in the field of mathematical physics, as well as an event of choice for the promotion of mathematical applications that address the most relevant problems found in industry. That makes this volume a suitable reading not only for researchers and graduate students with an interest in the field but for practitioners as well.
Author: Helge Holden
Publisher: American Mathematical Soc.
ISBN: 0821875744
Category : Mathematics
Languages : en
Pages : 409
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Book Description
This volume contains twenty contributions in the area of mathematical physics where Fritz Gesztesy made profound contributions. There are three survey papers in spectral theory, differential equations, and mathematical physics, which highlight, in particu
Author: Valentin A. Zagrebnov
Publisher: Springer Nature
ISBN: 303156720X
Category :
Languages : en
Pages : 879
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Book Description
Author: Ronald Hagen
Publisher: CRC Press
ISBN: 9780824704605
Category : Mathematics
Languages : en
Pages : 388
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Book Description
"Analyzes algebras of concrete approximation methods detailing prerequisites, local principles, and lifting theorems. Covers fractality and Fredholmness. Explains the phenomena of the asymptotic splitting of the singular values, and more."
