On the Description of Extensions of a Positive-Definite Operator Function PDF Download

Author: M. L. Gorbachuk
Publisher:
ISBN:
Category :
Languages : en
Pages : 17

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Author: Palle Jorgensen
Publisher: Springer
ISBN: 331939780X
Category : Mathematics
Languages : en
Pages : 255

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Book Description
This monograph deals with the mathematics of extending given partial data-sets obtained from experiments; Experimentalists frequently gather spectral data when the observed data is limited, e.g., by the precision of instruments; or by other limiting external factors. Here the limited information is a restriction, and the extensions take the form of full positive definite function on some prescribed group. It is therefore both an art and a science to produce solid conclusions from restricted or limited data. While the theory of is important in many areas of pure and applied mathematics, it is difficult for students and for the novice to the field, to find accessible presentations which cover all relevant points of view, as well as stressing common ideas and interconnections. We have aimed at filling this gap, and we have stressed hands-on-examples.

Author: Jussi Behrndt
Publisher: Springer Nature
ISBN: 3030367142
Category : Mathematics
Languages : en
Pages : 772

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Book Description
This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension theory of symmetric operators and relations, spectral characterizations of selfadjoint operators in terms of the analytic properties of Weyl functions, form methods for semibounded operators, and functional analytic models for reproducing kernel Hilbert spaces. Further, it illustrates these abstract methods for various applications, including Sturm-Liouville operators, canonical systems of differential equations, and multidimensional Schrödinger operators, where the abstract Weyl function appears as either the classical Titchmarsh-Weyl coefficient or the Dirichlet-to-Neumann map. The book is a valuable reference text for researchers in the areas of differential equations, functional analysis, mathematical physics, and system theory. Moreover, thanks to its detailed exposition of the theory, it is also accessible and useful for advanced students and researchers in other branches of natural sciences and engineering.

Author: I. Gohberg
Publisher: Birkhäuser
ISBN: 3034885962
Category : Science
Languages : en
Pages : 223

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Author: I. Gohberg
Publisher: Birkhäuser
ISBN: 3034877013
Category : Science
Languages : en
Pages : 311

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Author: Joseph A. Ball
Publisher: Springer Science & Business Media
ISBN: 3034601581
Category : Mathematics
Languages : en
Pages : 624

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Book Description
This is the first volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications.

Author: Matthias Langer
Publisher: Springer Science & Business Media
ISBN: 3764375167
Category : Mathematics
Languages : en
Pages : 403

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Book Description
A colloquium on operator theory was held in Vienna, Austria, in March 2004, on the occasion of the retirement of Heinz Langer, a leading expert in operator theory and indefinite inner product spaces. The book contains fifteen refereed articles reporting on recent and original results in various areas of operator theory, all of them related with the work of Heinz Langer. The topics range from abstract spectral theory in Krein spaces to more concrete applications, such as boundary value problems, the study of orthogonal functions, or moment problems. The book closes with a historical survey paper.

Author: Dym
Publisher: Birkhäuser
ISBN: 3034854250
Category : Science
Languages : en
Pages : 377

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Book Description
This volume contains the proceedings of the Workshop on app1ications of linear operator theory to systems and networks, which was held at the Weizmann Institute of Science in the third week of June, 19S3, just be fore the MTNS Conference in Beersheva. For a 10ng time these subjects were studied indepen dent1y by mathematica1 ana1ysts and e1ectrica1 engineers. Never the1ess, in spite of the lack of communication, these two groups often deve10ped parallel theories, though in different languages, at different levels of genera1ity and typica11y quite different motivations. In the last severa1 years each side has become aware of the work of the other and there is a seeming1y ever increasing invo1vement of the abstract theories of factorization, extension and interpolation of operators (and operator/matrix va1ued functions) to the design and analysis of systems and net works. Moreover, the problems encountered in e1ectrica1 engineering have genera ted new mathematica1 problems, new approaches, and usefu1 new formu1ations. The papers contained in this volume constitute a more than representative se1ection of the presented talks and dis cussion at the workshop, and hopefu11y will also serve to give a reasonably accurate picture of the problems which are under active study today and the techniques which are used to deal with them."

Author: John R. McMullen
Publisher: American Mathematical Soc.
ISBN: 0821818171
Category : Mathematics
Languages : en
Pages : 79

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Author: Vadim Adamyan
Publisher: Springer Science & Business Media
ISBN: 3764399198
Category : Mathematics
Languages : en
Pages : 497

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Book Description
This is the first of two volumes containing peer-reviewed research and survey papers based on talks at the International Conference on Modern Analysis and Applications. The papers describe the contemporary development of subjects influenced by Mark Krein.