Methods of noncommutative analysis: theory and applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Walter de Gruyter
1995
|
| Schriftenreihe: | De Gruyter studies in mathematics
22 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 |
| Beschreibung: | Includes bibliographical references and index ""Preface""; ""I Elementary Notions of Noncommutative Analysis""; ""1 Some Situations where Functions of Noncommuting Operators Arise""; ""1.1 Nonautonomous Linear Differential Equations of First Order. T-Exponentials""; ""1.2 Operators of Quantum Mechanics. Creation and Annihilation Operators""; ""1.3 Differential and Integral Operators""; ""1.4 Problems of Perturbation Theory""; ""1.5 Multiplication Law in Lie Groups""; ""1.6 Eigenfunctions and Eigenvalues of the Quantum Oscillator""; ""1.7 T-Exponentials, Trotter Formulas, and Path Integrals"" ""2 Functions of Noncommuting Operators: the Construction and Main Properties""""2.1 Motivations""; ""2.2 The Definition and the Uniqueness Theorem""; ""2.3 Basic Properties""; ""2.4 Tempered Symbols and Generators of Tempered Groups""; ""2.5 The Influence of the Symbol Classes on the Properties of Generators""; ""2.6 Weyl Quantization""; ""3 Noncommutative Differential Calculus""; ""3.1 The Derivation Formula""; ""3.2 The Daletskii-Krein Formula""; ""3.3 Higher-Order Expansions""; ""3.4 Permutation of Feynman Indices""; ""3.5 The Composite Function Formula"" ""4 The Campbell-Hausdorff Theorem and Dynkinâ€?s Formula""""4.1 Statement of the Problem""; ""4.2 The Commutation Operation""; ""4.3 A Closed Formula for In (eBeA)""; ""4.4 A Closed Formula for the Logarithm of a T-Exponential""; ""5 Summary: Rules of â€Operator Arithmeticâ€? and Some Standard Techniques""; ""5.1 Notation""; ""5.2 Rules""; ""5.3 Standard Techniques""; ""II Method of Ordered Representation""; ""1 Ordered Representation: Definition and Main Property""; ""1.1 Wick Normal Form""; ""1.2 Ordered Representation and Theorem on Products""; ""1.3 Reduction to Normal Form"" ""2 Some Examples""""2.1 Functions of the Operators x and â€? ihÓ?/dÓ?""; ""2.2 Perturbed Heisenberg Relations""; ""2.3 Examples of Nonlinear Commutation Relations""; ""2.4 Lie Commutation Relations""; ""2.5 Graded Lie Algebras""; ""3 Evaluation of the Ordered Representation Operators""; ""3.1 Equations for the Ordered Representation Operators""; ""3.2 How to Obtain the Solution""; ""3.3 Semilinear Commutation Relations""; ""4 The Jacobi Condition and Poincaré-Birkhoff-Witt Theorem""; ""4.1 Ordered Representation of Relation Systems and the Jacobi Condition"" ""4.2 The Poincaré-Birkhoff-Witt Theorem""""4.3 Verification of the Jacobi Condition: Two Examples""; ""5 The Ordered Representations, Jacobi Condition, and the Yang-Baxter Equation""; ""6 Representations of Lie Groups and Functions of Their Generators""; ""6.1 Conditions on the Representation""; ""6.2 Hilbert Scales""; ""6.3 Symbol Spaces""; ""6.4 Symbol Classes: More Suitable for Asymptotic Problems""; ""III Noncommutative Analysis and Differential Equations""; ""1 Preliminaries""; ""1.1 Heavisideâ€?s Operator Method for Differential Equations with Constant Coefficients"" |
| Beschreibung: | x, 373 pages |
| ISBN: | 9783110813548 3110813548 1306275261 9781306275262 3110146320 9783110146325 |
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| 100 | 1 | |a Nazaĭkinskiĭ, V. E. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Methods of noncommutative analysis |b theory and applications |c Vladimir E. Nazaikinskii, Victor E. Shatalov, Boris Yu. Sternin |
| 264 | 1 | |a Berlin |b Walter de Gruyter |c 1995 | |
| 300 | |a x, 373 pages | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a De Gruyter studies in mathematics |v 22 | |
| 500 | |a Includes bibliographical references and index | ||
| 500 | |a ""Preface""; ""I Elementary Notions of Noncommutative Analysis""; ""1 Some Situations where Functions of Noncommuting Operators Arise""; ""1.1 Nonautonomous Linear Differential Equations of First Order. T-Exponentials""; ""1.2 Operators of Quantum Mechanics. Creation and Annihilation Operators""; ""1.3 Differential and Integral Operators""; ""1.4 Problems of Perturbation Theory""; ""1.5 Multiplication Law in Lie Groups""; ""1.6 Eigenfunctions and Eigenvalues of the Quantum Oscillator""; ""1.7 T-Exponentials, Trotter Formulas, and Path Integrals"" | ||
| 500 | |a ""2 Functions of Noncommuting Operators: the Construction and Main Properties""""2.1 Motivations""; ""2.2 The Definition and the Uniqueness Theorem""; ""2.3 Basic Properties""; ""2.4 Tempered Symbols and Generators of Tempered Groups""; ""2.5 The Influence of the Symbol Classes on the Properties of Generators""; ""2.6 Weyl Quantization""; ""3 Noncommutative Differential Calculus""; ""3.1 The Derivation Formula""; ""3.2 The Daletskii-Krein Formula""; ""3.3 Higher-Order Expansions""; ""3.4 Permutation of Feynman Indices""; ""3.5 The Composite Function Formula"" | ||
| 500 | |a ""4 The Campbell-Hausdorff Theorem and Dynkinâ€?s Formula""""4.1 Statement of the Problem""; ""4.2 The Commutation Operation""; ""4.3 A Closed Formula for In (eBeA)""; ""4.4 A Closed Formula for the Logarithm of a T-Exponential""; ""5 Summary: Rules of â€Operator Arithmeticâ€? and Some Standard Techniques""; ""5.1 Notation""; ""5.2 Rules""; ""5.3 Standard Techniques""; ""II Method of Ordered Representation""; ""1 Ordered Representation: Definition and Main Property""; ""1.1 Wick Normal Form""; ""1.2 Ordered Representation and Theorem on Products""; ""1.3 Reduction to Normal Form"" | ||
| 500 | |a ""2 Some Examples""""2.1 Functions of the Operators x and â€? ihÓ?/dÓ?""; ""2.2 Perturbed Heisenberg Relations""; ""2.3 Examples of Nonlinear Commutation Relations""; ""2.4 Lie Commutation Relations""; ""2.5 Graded Lie Algebras""; ""3 Evaluation of the Ordered Representation Operators""; ""3.1 Equations for the Ordered Representation Operators""; ""3.2 How to Obtain the Solution""; ""3.3 Semilinear Commutation Relations""; ""4 The Jacobi Condition and Poincaré-Birkhoff-Witt Theorem""; ""4.1 Ordered Representation of Relation Systems and the Jacobi Condition"" | ||
| 500 | |a ""4.2 The Poincaré-Birkhoff-Witt Theorem""""4.3 Verification of the Jacobi Condition: Two Examples""; ""5 The Ordered Representations, Jacobi Condition, and the Yang-Baxter Equation""; ""6 Representations of Lie Groups and Functions of Their Generators""; ""6.1 Conditions on the Representation""; ""6.2 Hilbert Scales""; ""6.3 Symbol Spaces""; ""6.4 Symbol Classes: More Suitable for Asymptotic Problems""; ""III Noncommutative Analysis and Differential Equations""; ""1 Preliminaries""; ""1.1 Heaviside�s Operator Method for Differential Equations with Constant Coefficients"" | ||
| 650 | 4 | |a Geometry, Differential | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Noncommutative algebras | |
| 650 | 7 | |a MATHEMATICS / Functional Analysis |2 bisacsh | |
| 650 | 7 | |a Geometry, Differential |2 fast | |
| 650 | 7 | |a Mathematical physics |2 fast | |
| 650 | 7 | |a Noncommutative algebras |2 fast | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Geometry, Differential | |
| 650 | 4 | |a Noncommutative algebras | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 0 | 7 | |a Nicht vertauschbarer Operator |0 (DE-588)4303614-4 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Shatalov, V. E.7001 L |e Sonstige |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804176598918758400 |
|---|---|
| any_adam_object | |
| author | Nazaĭkinskiĭ, V. E. |
| author_facet | Nazaĭkinskiĭ, V. E. |
| author_role | aut |
| author_sort | Nazaĭkinskiĭ, V. E. |
| author_variant | v e n ve ven |
| building | Verbundindex |
| bvnumber | BV043774209 |
| collection | ZDB-4-EBA |
| ctrlnum | (ZDB-4-EBA)ocn811372212 (OCoLC)811372212 (DE-599)BVBBV043774209 |
| dewey-full | 515/.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.72 |
| dewey-search | 515/.72 |
| dewey-sort | 3515 272 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043774209 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:34:44Z |
| institution | BVB |
| isbn | 9783110813548 3110813548 1306275261 9781306275262 3110146320 9783110146325 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029185269 |
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| physical | x, 373 pages |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 1995 |
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| publisher | Walter de Gruyter |
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| series2 | De Gruyter studies in mathematics |
| spelling | Nazaĭkinskiĭ, V. E. Verfasser aut Methods of noncommutative analysis theory and applications Vladimir E. Nazaikinskii, Victor E. Shatalov, Boris Yu. Sternin Berlin Walter de Gruyter 1995 x, 373 pages txt rdacontent c rdamedia cr rdacarrier De Gruyter studies in mathematics 22 Includes bibliographical references and index ""Preface""; ""I Elementary Notions of Noncommutative Analysis""; ""1 Some Situations where Functions of Noncommuting Operators Arise""; ""1.1 Nonautonomous Linear Differential Equations of First Order. T-Exponentials""; ""1.2 Operators of Quantum Mechanics. Creation and Annihilation Operators""; ""1.3 Differential and Integral Operators""; ""1.4 Problems of Perturbation Theory""; ""1.5 Multiplication Law in Lie Groups""; ""1.6 Eigenfunctions and Eigenvalues of the Quantum Oscillator""; ""1.7 T-Exponentials, Trotter Formulas, and Path Integrals"" ""2 Functions of Noncommuting Operators: the Construction and Main Properties""""2.1 Motivations""; ""2.2 The Definition and the Uniqueness Theorem""; ""2.3 Basic Properties""; ""2.4 Tempered Symbols and Generators of Tempered Groups""; ""2.5 The Influence of the Symbol Classes on the Properties of Generators""; ""2.6 Weyl Quantization""; ""3 Noncommutative Differential Calculus""; ""3.1 The Derivation Formula""; ""3.2 The Daletskii-Krein Formula""; ""3.3 Higher-Order Expansions""; ""3.4 Permutation of Feynman Indices""; ""3.5 The Composite Function Formula"" ""4 The Campbell-Hausdorff Theorem and Dynkinâ€?s Formula""""4.1 Statement of the Problem""; ""4.2 The Commutation Operation""; ""4.3 A Closed Formula for In (eBeA)""; ""4.4 A Closed Formula for the Logarithm of a T-Exponential""; ""5 Summary: Rules of â€Operator Arithmeticâ€? and Some Standard Techniques""; ""5.1 Notation""; ""5.2 Rules""; ""5.3 Standard Techniques""; ""II Method of Ordered Representation""; ""1 Ordered Representation: Definition and Main Property""; ""1.1 Wick Normal Form""; ""1.2 Ordered Representation and Theorem on Products""; ""1.3 Reduction to Normal Form"" ""2 Some Examples""""2.1 Functions of the Operators x and â€? ihÓ?/dÓ?""; ""2.2 Perturbed Heisenberg Relations""; ""2.3 Examples of Nonlinear Commutation Relations""; ""2.4 Lie Commutation Relations""; ""2.5 Graded Lie Algebras""; ""3 Evaluation of the Ordered Representation Operators""; ""3.1 Equations for the Ordered Representation Operators""; ""3.2 How to Obtain the Solution""; ""3.3 Semilinear Commutation Relations""; ""4 The Jacobi Condition and Poincaré-Birkhoff-Witt Theorem""; ""4.1 Ordered Representation of Relation Systems and the Jacobi Condition"" ""4.2 The Poincaré-Birkhoff-Witt Theorem""""4.3 Verification of the Jacobi Condition: Two Examples""; ""5 The Ordered Representations, Jacobi Condition, and the Yang-Baxter Equation""; ""6 Representations of Lie Groups and Functions of Their Generators""; ""6.1 Conditions on the Representation""; ""6.2 Hilbert Scales""; ""6.3 Symbol Spaces""; ""6.4 Symbol Classes: More Suitable for Asymptotic Problems""; ""III Noncommutative Analysis and Differential Equations""; ""1 Preliminaries""; ""1.1 Heavisideâ€?s Operator Method for Differential Equations with Constant Coefficients"" Geometry, Differential Mathematical physics Noncommutative algebras MATHEMATICS / Functional Analysis bisacsh Geometry, Differential fast Mathematical physics fast Noncommutative algebras fast Mathematische Physik Nicht vertauschbarer Operator (DE-588)4303614-4 gnd rswk-swf Nicht vertauschbarer Operator (DE-588)4303614-4 s 1\p DE-604 Shatalov, V. E.7001 L Sonstige oth 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nazaĭkinskiĭ, V. E. Methods of noncommutative analysis theory and applications Geometry, Differential Mathematical physics Noncommutative algebras MATHEMATICS / Functional Analysis bisacsh Geometry, Differential fast Mathematical physics fast Noncommutative algebras fast Mathematische Physik Nicht vertauschbarer Operator (DE-588)4303614-4 gnd |
| subject_GND | (DE-588)4303614-4 |
| title | Methods of noncommutative analysis theory and applications |
| title_auth | Methods of noncommutative analysis theory and applications |
| title_exact_search | Methods of noncommutative analysis theory and applications |
| title_full | Methods of noncommutative analysis theory and applications Vladimir E. Nazaikinskii, Victor E. Shatalov, Boris Yu. Sternin |
| title_fullStr | Methods of noncommutative analysis theory and applications Vladimir E. Nazaikinskii, Victor E. Shatalov, Boris Yu. Sternin |
| title_full_unstemmed | Methods of noncommutative analysis theory and applications Vladimir E. Nazaikinskii, Victor E. Shatalov, Boris Yu. Sternin |
| title_short | Methods of noncommutative analysis |
| title_sort | methods of noncommutative analysis theory and applications |
| title_sub | theory and applications |
| topic | Geometry, Differential Mathematical physics Noncommutative algebras MATHEMATICS / Functional Analysis bisacsh Geometry, Differential fast Mathematical physics fast Noncommutative algebras fast Mathematische Physik Nicht vertauschbarer Operator (DE-588)4303614-4 gnd |
| topic_facet | Geometry, Differential Mathematical physics Noncommutative algebras MATHEMATICS / Functional Analysis Mathematische Physik Nicht vertauschbarer Operator |
| work_keys_str_mv | AT nazaikinskiive methodsofnoncommutativeanalysistheoryandapplications AT shatalovve7001l methodsofnoncommutativeanalysistheoryandapplications |