Methods of noncommutative analysis :: theory and applications /
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; New York :
Walter de Gruyter,
1995.
|
| Schriftenreihe: | De Gruyter studies in mathematics ;
22. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 1 online resource (x, 373 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9783110813548 3110813548 1306275261 9781306275262 |
Internformat
MARC
| LEADER | 00000cam a2200000Ma 4500 | ||
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| 100 | 1 | |a Nazaĭkinskiĭ, V. E. | |
| 245 | 1 | 0 | |a Methods of noncommutative analysis : |b theory and applications / |c Vladimir E. Nazaikinskii, Victor E. Shatalov, Boris Yu. Sternin. |
| 260 | |a Berlin ; |a New York : |b Walter de Gruyter, |c 1995. | ||
| 300 | |a 1 online resource (x, 373 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter studies in mathematics ; |v 22 | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |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 | |
| 505 | 8 | |a 2 Functions of Noncommuting Operators: the Construction and Main Properties2.1 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 | |
| 505 | 8 | |a 4 The Campbell-Hausdorff Theorem and Dynkinâ€?s Formula4.1 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 | |
| 505 | 8 | |a 2 Some Examples2.1 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 | |
| 505 | 8 | |a 4.2 The Poincaré-Birkhoff-Witt Theorem4.3 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 | |
| 546 | |a English. | ||
| 650 | 0 | |a Geometry, Differential. |0 http://id.loc.gov/authorities/subjects/sh85054146 | |
| 650 | 0 | |a Noncommutative algebras. |0 http://id.loc.gov/authorities/subjects/sh85092241 | |
| 650 | 0 | |a Mathematical physics. |0 http://id.loc.gov/authorities/subjects/sh85082129 | |
| 650 | 6 | |a Géométrie différentielle. | |
| 650 | 6 | |a Algèbres non commutatives. | |
| 650 | 6 | |a Physique mathématique. | |
| 650 | 7 | |a MATHEMATICS |x Functional Analysis. |2 bisacsh | |
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| 650 | 7 | |a Mathematical physics |2 fast | |
| 650 | 7 | |a Noncommutative algebras |2 fast | |
| 700 | 1 | |a Shatalov, V. E. |q (Viktor Evgenʹevich) |1 https://id.oclc.org/worldcat/entity/E39PCjBPtQc6r49wJFrDtFHmcX |0 http://id.loc.gov/authorities/names/n88189541 | |
| 700 | 1 | |a Sternin, B. I︠U︡. | |
| 758 | |i has work: |a Methods of Noncommutative Analysis (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFPM9mm8YcKVgtCqqPtk6q |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
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| 830 | 0 | |a De Gruyter studies in mathematics ; |v 22. |0 http://id.loc.gov/authorities/names/n83742913 | |
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| author | Nazaĭkinskiĭ, V. E. |
| author2 | Shatalov, V. E. (Viktor Evgenʹevich) Sternin, B. I︠U︡ |
| author2_role | |
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| contents | 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 Properties2.1 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 Formula4.1 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 Examples2.1 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 Theorem4.3 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 |
| ctrlnum | (OCoLC)811372212 |
| 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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| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:24:57Z |
| institution | BVB |
| isbn | 9783110813548 3110813548 1306275261 9781306275262 |
| language | English |
| oclc_num | 811372212 |
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| series | De Gruyter studies in mathematics ; |
| series2 | De Gruyter studies in mathematics ; |
| spelling | Nazaĭkinskiĭ, V. E. Methods of noncommutative analysis : theory and applications / Vladimir E. Nazaikinskii, Victor E. Shatalov, Boris Yu. Sternin. Berlin ; New York : Walter de Gruyter, 1995. 1 online resource (x, 373 pages) text txt rdacontent computer c rdamedia online resource 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 Properties2.1 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 Formula4.1 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 Examples2.1 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 Theorem4.3 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 English. Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Noncommutative algebras. http://id.loc.gov/authorities/subjects/sh85092241 Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Géométrie différentielle. Algèbres non commutatives. Physique mathématique. MATHEMATICS Functional Analysis. bisacsh Geometry, Differential fast Mathematical physics fast Noncommutative algebras fast Shatalov, V. E. (Viktor Evgenʹevich) https://id.oclc.org/worldcat/entity/E39PCjBPtQc6r49wJFrDtFHmcX http://id.loc.gov/authorities/names/n88189541 Sternin, B. I︠U︡. has work: Methods of Noncommutative Analysis (Text) https://id.oclc.org/worldcat/entity/E39PCFPM9mm8YcKVgtCqqPtk6q https://id.oclc.org/worldcat/ontology/hasWork Print version: 9781306275262 De Gruyter studies in mathematics ; 22. http://id.loc.gov/authorities/names/n83742913 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=560593 Volltext |
| spellingShingle | Nazaĭkinskiĭ, V. E. Methods of noncommutative analysis : theory and applications / De Gruyter studies in mathematics ; 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 Properties2.1 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 Formula4.1 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 Examples2.1 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 Theorem4.3 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. http://id.loc.gov/authorities/subjects/sh85054146 Noncommutative algebras. http://id.loc.gov/authorities/subjects/sh85092241 Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Géométrie différentielle. Algèbres non commutatives. Physique mathématique. MATHEMATICS Functional Analysis. bisacsh Geometry, Differential fast Mathematical physics fast Noncommutative algebras fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85054146 http://id.loc.gov/authorities/subjects/sh85092241 http://id.loc.gov/authorities/subjects/sh85082129 |
| 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. http://id.loc.gov/authorities/subjects/sh85054146 Noncommutative algebras. http://id.loc.gov/authorities/subjects/sh85092241 Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Géométrie différentielle. Algèbres non commutatives. Physique mathématique. MATHEMATICS Functional Analysis. bisacsh Geometry, Differential fast Mathematical physics fast Noncommutative algebras fast |
| topic_facet | Geometry, Differential. Noncommutative algebras. Mathematical physics. Géométrie différentielle. Algèbres non commutatives. Physique mathématique. MATHEMATICS Functional Analysis. Geometry, Differential Mathematical physics Noncommutative algebras |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=560593 |
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