Regular functions of a quaternionic variable / / Graziano Gentili, Caterina Stoppato, Daniele C. Struppa

• Record Nr.: UNISA996490343903316
• Autore: Gentili Graziano
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2022]; ©2022
• ISBN: 3-031-07531-5
• Edizione: [2nd ed.]
• Descrizione fisica: 1 online resource (302 pages)
• Collana: Springer Monographs in Mathematics
• Disciplina: 515.98
• Soggetti: Functions, Quaternion; Quaternions; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Preface -- Preface to the Second Edition -- Introduction -- Contents -- 1 Definitions and Basic Results -- 1.1 Regular Functions -- 1.2 Affine Representation -- 1.3 Extension Results and Local Representation -- 1.4 Algebraic Structure -- Bibliographic Notes -- 2 Regular Power Series -- 2.1 The Distance σ -- 2.2 Convergence of Power Series Centered at p -- 2.3 Series Expansion at p and Analyticity -- Bibliographic Notes -- 3 Zeros -- 3.1 Basic Properties of the Zeros -- 3.2 Algebraic Properties of the Zeros -- 3.3 Topological Properties of the Zeros -- 3.4 On the Roots of Quaternions -- 3.5 Factorization of Polynomials -- 3.6 Multiplicity -- 3.7 Division Algorithm and Bezout Theorem -- 3.8 Gröbner Bases for Quaternionic Polynomials -- Bibliographic Notes -- 4 Infinite Products -- 4.1 Infinite Products of Quaternions -- 4.2 The Principal Branch of Quaternionic Logarithm -- 4.3 Infinite Products of Functions Defined on ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper H) /StPNE pdfmark [/StBMC pdfmarkHps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 4.4 Convergence of an Infinite-Product -- 4.5 Convergence-Producing Regular Factors -- 4.6 Weierstrass Factorization Theorem -- Bibliographic Notes -- 5 Singularities -- 5.1 Regular Reciprocal and Quotients -- 5.2 Laurent Series and Expansion -- 5.3 Classification of Singularities -- 5.4 Poles and Quotients -- 5.5 ; Casorati-Weierstrass Theorem -- Bibliographic Notes -- 6 Integral Representations -- 6.1 Cauchy Theorem and Morera Theorem -- 6.2 Cauchy Integral Formula -- 6.3 Pompeiu Formula -- 6.4 Derivatives Using the Cauchy Formula -- 6.5 Coefficients of the Laurent Series Expansion -- 6.6 Argument Principle -- Bibliographic Notes -- 7 Maximum Modulus Theorem and Applications -- 7.1 Maximum and Minimum Modulus -- 7.2 Open Mapping Theorem -- 7.3 Real Parts of Regular Functions.; 7.4 Phragmén-Lindelöf Principles -- 7.5 An Ehrenpreis-Malgrange Lemma -- Bibliographic Notes -- 8 Spherical Series and Differential -- 8.1 Spherical Series and Expansions -- 8.2 Integral Formulas and Cauchy Estimates -- 8.3 Symmetric Analyticity -- 8.4 Differentiating Regular Functions -- 8.5 Rank of the Differential -- Bibliographic Notes -- 9 Fractional Transformations and the Unit Ball -- 9.1 Transformations of the Quaternionic Space -- 9.2 Regular Fractional Transformations -- 9.3 Transformations of the Quaternionic Riemann Sphere -- 9.4 Schwarz Lemma and Transformations of the Unit Ball -- 9.5 Rigidity and a Boundary Schwarz Lemma -- 9.6 Borel-Carathéodory Theorem -- 9.7 Bohr Theorem -- Bibliographic Notes -- 10 Generalizations -- 10.1 Direct Generalizations to Algebras Other Than ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper H) /StPNE pdfmark [/StBMC pdfmarkHps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 10.1.1 The Case of Octonions -- 10.1.2 The Case of ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R 3) /StPNE pdfmark [/StBMC pdfmarkR3ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 10.1.3 The Slice Monogenic Case -- 10.2 Slice Functions Over ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper H) /StPNE pdfmark [/StBMC pdfmarkHps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark and Other Alternative Real Algebras -- 10.3 An Alternative Approach to Slice Regularity -- 11 Function Theory Over Non-symmetric Slice Domains -- 11.1 Spherical Value and Derivative -- 11.2 Locally Slice Functions and their Algebraic Structure -- 11.3 Zero Sets -- 11.4 Quotients -- 11.5 Factorization of Zeros -- 11.6 Applications of Factorization -- 11.7 Semiregular Functions -- 11.8 Minimum Modulus Principle and Open Mapping Theorem -- 11.9 Integral Representation -- 11.10 Spherical Series Expansions.; Bibliographic Notes -- 12 Applications -- 12.1 Applications in Functional Analysis -- 12.1.1 Quaternionic Functional Calculus -- 12.1.2 Some Quaternionic Function Spaces -- 12.2 Applications in Differential Geometry -- 12.2.1 Orthogonal Complex Structures Induced by Regular Functions -- 12.2.2 A Direct Approach to Quaternionic Manifolds -- 12.3 Applications in Spatial Kinematics -- 12.3.1 Rational Rotation-Minimizing Frame Curves -- 12.3.2 Motion Polynomials over Dual Quaternions -- References -- Index.