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  • 1
    UID:
    almafu_BV004464660
    Format: 40 Seiten.
    ISBN: 951-41-0636-9
    Series Statement: Suomalainen Tiedeakatemia 〈Helsinki〉: [Annales Academiae Scientiarum Fennicae / A / 1 / Dissertationes] 79
    Note: Zugl.: Helsinki, Univ., Diss., 1990
    Language: English
    Subjects: Mathematics
    RVK:
    RVK:
    Keywords: Matrix ; Zerlegung ; Indefinites Skalarprodukt ; Hochschulschrift ; Hochschulschrift ; Hochschulschrift ; Hochschulschrift
    Author information: Hassi, Seppo
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  • 2
    Online Resource
    Online Resource
    Cham : Springer Nature | Cham :Springer International Publishing :
    UID:
    almafu_9959250211002883
    Format: 1 online resource (IX, 772 p. 1 illus.)
    Edition: 1st ed. 2020.
    ISBN: 3-030-36714-2
    Series Statement: Monographs in Mathematics, 108
    Content: 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.
    Note: Linear relations -- Boundary triplets and Weyl functions -- Spectra and Weyl functions -- Operator models -- Nonnegative selfadjoint extensions -- Sturm-Liouville operators -- Canonical systems -- Schrodinger operators -- Sums of closed subspaces in a Hilbert space -- Factorization of bounded linear operators -- Integral representations of Carathéodory functions -- The integral representation of Nevanlinna functions. , English
    Additional Edition: ISBN 3-030-36713-4
    Language: English
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  • 3
    UID:
    gbv_1778475752
    Format: 1 Online-Ressource (772 p.)
    ISBN: 9783030367145
    Series Statement: Monographs in Mathematics
    Content: 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
    Note: English
    Language: English
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  • 4
    UID:
    almahu_9948219196402882
    Format: IX, 772 p. 1 illus. , online resource.
    Edition: 1st ed. 2020.
    ISBN: 9783030367145
    Series Statement: Monographs in Mathematics, 108
    Content: 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.
    Note: Linear relations -- Boundary triplets and Weyl functions -- Spectra and Weyl functions -- Operator models -- Nonnegative selfadjoint extensions -- Sturm-Liouville operators -- Canonical systems -- Schrodinger operators -- Sums of closed subspaces in a Hilbert space -- Factorization of bounded linear operators -- Integral representations of Carathéodory functions -- The integral representation of Nevanlinna functions.
    In: Springer eBooks
    Additional Edition: Printed edition: ISBN 9783030367138
    Additional Edition: Printed edition: ISBN 9783030367152
    Additional Edition: Printed edition: ISBN 9783030367169
    Language: English
    Subjects: Mathematics
    RVK:
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  • 5
    UID:
    almahu_9948233628402882
    Format: 1 online resource (xii, 298 pages) : , digital, PDF file(s).
    ISBN: 9781139135061 (ebook)
    Series Statement: London Mathematical Society lecture note series ; 404
    Content: Presented in this volume are a number of new results concerning the extension theory and spectral theory of unbounded operators using the recent notions of boundary triplets and boundary relations. This approach relies on linear single-valued and multi-valued maps, isometric in a Krein space sense, and offers a basic framework for recent developments in system theory. Central to the theory are analytic tools such as Weyl functions, including Titchmarsh-Weyl m-functions and Dirichlet-to-Neumann maps. A wide range of topics is considered in this context from the abstract to the applied, including boundary value problems for ordinary and partial differential equations; infinite-dimensional perturbations; local point-interactions; boundary and passive control state/signal systems; extension theory of accretive, sectorial and symmetric operators; and Calkin's abstract boundary conditions. This accessible treatment of recent developments, written by leading researchers, will appeal to a broad range of researchers, students and professionals.
    Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015). , 1. John Williams Calkin: a short biography / S. Hassi, H.S.V. de Snoo and F.H. Szafraniec -- 2. On Calkin's abstract symmetric boundary conditions / S. Hassi and H.L. Wietsma -- 3. Boundary triplets and maximal accretive extensions of sectorial operators / Y. Arlinskiĭ -- 4. Boundary control state/signal systems and boundary triplets / D.Z. Arov, M. Kurula and O.J. Staffans -- 5. Passive state/signal systems and conservative boundary relations / D.Z. Arov, M. Kurula and O.J. Staffans -- 6. Elliptic operators, Dirichlet-to-Neumann maps and quasi boundary triples / J. Behrndt and M. Langer -- 7. Boundary triplets and Weyl functions. Recent developments / V.A. Derkach, S. Hassi, M.M. Malamud and H.S.V. de Snoo -- 8. Extension theory for elliptic partial differential operators with pseudodifferential methods / G. Grubb -- 9. Dirac structures and boundary relations / S. Hassi, A.J. van der Schaft, H.S.V. de Snoo and H.J. Zwart -- 10. Naĭmark dilations and Naĭmark extensions in favour of moment problems / F.H. Szafraniec.
    Additional Edition: Print version: ISBN 9781107606111
    Language: English
    Subjects: Mathematics
    RVK:
    Keywords: Konferenzschrift
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  • 6
    Online Resource
    Online Resource
    Cham :Springer International Publishing AG,
    UID:
    almahu_9949301187202882
    Format: 1 online resource (775 pages)
    ISBN: 9783030367145
    Series Statement: Monographs in Mathematics Ser. ; v.108
    Note: Intro -- Contents -- Preface -- 1 Introduction -- 2 Linear Relations in Hilbert Spaces -- 1.1 Elementary facts about linear relations -- 1.2 Spectra, resolvent sets, and points of regular type -- 1.3 Adjoint relations -- 1.4 Symmetric relations -- 1.5 Self-adjoint relations -- 1.6 Maximal dissipative and accumulative relations -- 1.7 Intermediate extensions and von Neumann's formulas -- 1.8 Adjoint relations and indefinite inner products -- 1.9 Convergence of sequences of relations -- 1.10 Parametric representations for relations -- 1.11 Resolvent operators with respect to a bounded operator -- 1.12 Nevanlinna families and their representations -- 3 Boundary Triplets and Weyl Functions -- 2.1 Boundary triplets -- 2.2 Boundary value problems -- 2.3 Associated γ-fields and Weyl functions -- 2.4 Existence and construction of boundary triplets -- 2.5 Transformations of boundary triplets -- 2.6 Kreın's formula for intermediate extensions -- 2.7 Kreın's formula for exit space extensions -- 2.8 Perturbation problems -- 4 Spectra, Simple Operators, and Weyl Functions -- 3.1 Analytic descriptions of minimal supports of Borel measures -- 3.2 Growth points of finite Borel measures -- 3.3 Spectra of self-adjoint relations -- 3.4 Simple symmetric operators -- 3.5 Eigenvalues and eigenspaces -- 3.6 Spectra and local minimality -- 3.7 Limit properties of Weyl functions -- 3.8 Spectra and local minimality for self-adjoint extensions -- 5 Operator Models for Nevanlinna Functions -- 4.1 Reproducing kernel Hilbert spaces -- 4.2 Realization of uniformly strict Nevanlinna functions -- 4.3 Realization of scalar Nevanlinna functions via L2-space models -- 4.4 Realization of Nevanlinna pairs and generalized resolvents -- 4.5 Kreın's formula for exit space extensions -- 4.6 Orthogonal coupling of boundary triplets. , 6 Boundary Triplets and Boundary Pairs for Semibounded Relations -- 5.1 Closed semibounded forms and their representations -- 5.2 Ordering and monotonicity -- 5.3 Friedrichs extensions of semibounded relations -- 5.4 Semibounded self-adjoint extensions and their lower bounds -- 5.5 Boundary triplets for semibounded relations -- 5.6 Boundary pairs and boundary triplets -- 7 Sturm-Liouville Operators -- 6.1 Sturm-Liouville differential expressions -- 6.2 Maximal and minimal Sturm-Liouville differential operators -- 6.3 Regular and limit-circle endpoints -- 6.4 The case of one limit-point endpoint -- 6.5 The case of two limit-point endpoints and interface conditions -- 6.6 Exit space extensions -- 6.7 Weyl functions and subordinate solutions -- 6.8 Semibounded Sturm-Liouville expressions in the regular case -- 6.9 Closed semibounded forms for Sturm-Liouville equations -- 6.10 Principal and nonprincipal solutions of Sturm-Liouville equations -- 6.11 Semibounded Sturm-Liouville operators and the limit-circle case -- 6.12 Semibounded Sturm-Liouville operators and the limit-point case -- 6.13 Integrable potentials -- 8 Canonical Systems of Differential Equations -- 7.1 Classes of integrable functions -- 7.2 Canonical systems of differential equations -- 7.3 Regular and quasiregular endpoints -- 7.4 Square-integrability of solutions of real canonical systems -- 7.5 Definite canonical systems -- 7.6 Maximal and minimal relations for canonical systems -- 7.7 Boundary triplets for the limit-circle case -- 7.8 Boundary triplets for the limit-point case -- 7.9 Weyl functions and subordinate solutions -- 7.10 Special classes of canonical systems -- 9 Schrödinger Operators on Bounded Domains -- 8.1 Rigged Hilbert spaces -- 8.2 Sobolev spaces, C2-domains, and trace operators -- 8.3 Trace maps for the maximal Schrödinger operator. , 8.4 A boundary triplet for the maximal Schrödinger operator -- 8.5 Semibounded Schrödinger operators -- 8.6 Coupling of Schrödinger operators -- 8.7 Bounded Lipschitz domains -- Integral Representations of Nevanlinna Functions -- A.1 Borel transforms and their Stieltjes inversion -- A.2 Scalar Nevanlinna functions -- A.3 Operator-valued integrals -- A.4 Operator-valued Nevanlinna functions -- A.5 Kac functions -- A.6 Stieltjes and inverse Stieltjes functions -- Self-adjoint Operators and Fourier Transforms -- B.1 The scalar case -- B.2 The vector case -- Sums of Closed Subspaces in Hilbert Spaces -- Factorization of Bounded Linear Operators -- Notes -- Bibliography -- List of Symbols -- Index.
    Additional Edition: Print version: Behrndt, Jussi Boundary Value Problems, Weyl Functions, and Differential Operators Cham : Springer International Publishing AG,c2020 ISBN 9783030367138
    Language: English
    Keywords: Electronic books.
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  • 7
    UID:
    almafu_BV046403689
    Format: 1 Online-Ressource (vii, 772 Seiten).
    ISBN: 978-3-030-36714-5
    Series Statement: Monographs in Mathematics 108
    Note: Erscheint als Open Access bei Springer
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-36713-8
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-36715-2
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-36716-9
    Language: English
    Subjects: Economics , Mathematics
    RVK:
    RVK:
    Keywords: Mathematik ; Operatortheorie ; Systemtheorie
    URL: Volltext  (kostenfrei)
    URL: Volltext  (kostenfrei)
    Author information: Behrndt, Jussi
    Author information: Hassi, Seppo
    Author information: Snoo, Hendrik S. V. de 1945-
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  • 8
    UID:
    almahu_BV047306228
    Format: vii, 772 Seiten.
    ISBN: 978-3-030-36713-8 , 978-3-030-36716-9
    Series Statement: Monographs in Mathematics Volume 108
    Note: Erscheint als Open Access bei Springer
    Additional Edition: Erscheint auch als Online-Ausgabe ISBN 978-3-030-36714-5
    Language: English
    Subjects: Economics , Mathematics
    RVK:
    RVK:
    Keywords: Mathematik ; Operatortheorie ; Systemtheorie
    Author information: Behrndt, Jussi.
    Author information: Hassi, Seppo.
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  • 9
    Online Resource
    Online Resource
    Cham :Springer International Publishing,
    UID:
    kobvindex_HPB1137830384
    Format: 1 online resource (IX, 772 p. 1 illus.) , online resource.
    Edition: 1st ed. 2020.
    ISBN: 9783030367145 , 3030367142 , 9783030367138 , 3030367134 , 9783030367152 , 3030367150 , 9783030367169 , 3030367169
    Series Statement: Monographs in Mathematics, 108
    Content: 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.
    Note: Linear relations -- Boundary triplets and Weyl functions -- Spectra and Weyl functions -- Operator models -- Nonnegative selfadjoint extensions -- Sturm-Liouville operators -- Canonical systems -- Schrodinger operators -- Sums of closed subspaces in a Hilbert space -- Factorization of bounded linear operators -- Integral representations of Carathéodory functions -- The integral representation of Nevanlinna functions.
    In: OAPEN (Open Access Publishing in European Networks)., OAPEN
    Additional Edition: 3-030-36713-4
    Language: English
    Keywords: Electronic books.
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  • 10
    UID:
    edocfu_BV046403689
    Format: 1 Online-Ressource (vii, 772 Seiten).
    ISBN: 978-3-030-36714-5
    Series Statement: Monographs in Mathematics 108
    Note: Erscheint als Open Access bei Springer
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-36713-8
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-36715-2
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-36716-9
    Language: English
    Subjects: Economics , Mathematics
    RVK:
    RVK:
    Keywords: Mathematik ; Operatortheorie ; Systemtheorie
    URL: Volltext  (kostenfrei)
    URL: Volltext  (kostenfrei)
    Author information: Behrndt, Jussi
    Author information: Hassi, Seppo
    Author information: Snoo, Hendrik S. V. de 1945-
    Library Location Call Number Volume/Issue/Year Availability
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