An introduction to multicomplex spaces and functions. ([2018?])
- Record Type:
- Book
- Title:
- An introduction to multicomplex spaces and functions. ([2018?])
- Main Title:
- An introduction to multicomplex spaces and functions
- Further Information:
- Note: G. Baley Price.
- Authors:
- Price, G. Baley (Griffith Baley), 1905-2006
- Contents:
- Cover -- Half Title -- Title Page -- Copyright Page -- FOREWORD -- PREFACE -- Table of Contents -- Chapter 1: THE BICOMPLEX SPACE -- 1. Introduction -- 2. C2: A Linear Space -- 3. C2: A Banach Space -- 4. Multiplication -- 5. Fractions and Quotients -- 6. The Idempotent Representation -- 7. Two Principal Ideals -- 8. The Auxiliary Complex Spaces -- 9. The Discus -- Chapter 2: FUNCTIONS DEFINED BY BICOMPLEX POWER SERIES -- 10. Introduction -- 11. Limits of Sequences -- 12. Infinite Series -- 13. Power Series -- 14. Functions Represented by Power Series -- 15. Holomorphic Functions of a Bicomplex Variable -- 16. Algebras of Holomorphic Functions -- 17. Elementary Functions -- 18. The Logarithm Function -- Chapter 3: DERIVATIVES AND HOLOMORPHIC FUNCTIONS -- 19. Introduction -- 20. Derivatives and the Stolz Condition -- 21. Differentiability Implies the Strong Stolz Condition -- 22. The Weak Stolz Condition Implies Differentiability -- 23. Differentiability: Necessary Conditions -- 24. Differentiability: Sufficient Conditions -- 25. Holomorphic and Differentiable Functions -- 26. The Calculus of Derivatives -- 27. The Taylor Series of a Holomorphic Function -- 28. Isomorphic Bicomplex Algebras and Cauchy-Riemann Matrices -- 29. Holomorphic Functions and Their Inverses -- Chapter 4: INTEGRALS AND HOLOMORPHIC FUNCTIONS -- 30. Introduction -- 31. Curves in C2 -- 32. Integrals of Functions with Values in C2 -- 33. The Fundamental Theorem of the Integral Calculus -- 34. Cauchy'sCover -- Half Title -- Title Page -- Copyright Page -- FOREWORD -- PREFACE -- Table of Contents -- Chapter 1: THE BICOMPLEX SPACE -- 1. Introduction -- 2. C2: A Linear Space -- 3. C2: A Banach Space -- 4. Multiplication -- 5. Fractions and Quotients -- 6. The Idempotent Representation -- 7. Two Principal Ideals -- 8. The Auxiliary Complex Spaces -- 9. The Discus -- Chapter 2: FUNCTIONS DEFINED BY BICOMPLEX POWER SERIES -- 10. Introduction -- 11. Limits of Sequences -- 12. Infinite Series -- 13. Power Series -- 14. Functions Represented by Power Series -- 15. Holomorphic Functions of a Bicomplex Variable -- 16. Algebras of Holomorphic Functions -- 17. Elementary Functions -- 18. The Logarithm Function -- Chapter 3: DERIVATIVES AND HOLOMORPHIC FUNCTIONS -- 19. Introduction -- 20. Derivatives and the Stolz Condition -- 21. Differentiability Implies the Strong Stolz Condition -- 22. The Weak Stolz Condition Implies Differentiability -- 23. Differentiability: Necessary Conditions -- 24. Differentiability: Sufficient Conditions -- 25. Holomorphic and Differentiable Functions -- 26. The Calculus of Derivatives -- 27. The Taylor Series of a Holomorphic Function -- 28. Isomorphic Bicomplex Algebras and Cauchy-Riemann Matrices -- 29. Holomorphic Functions and Their Inverses -- Chapter 4: INTEGRALS AND HOLOMORPHIC FUNCTIONS -- 30. Introduction -- 31. Curves in C2 -- 32. Integrals of Functions with Values in C2 -- 33. The Fundamental Theorem of the Integral Calculus -- 34. Cauchy's Integral Theorem: A Special Case -- 35. Existence of Primitives -- 36. Cauchy's Integral Theorem: The General Case -- 37. Integrals Independent of the Path -- 38. Integrals and the Idempotent Representation -- 39. Cauchy's Integral Theorem and the Idempotent Representation -- 40. Cauchy's Integral Formula -- 41. Taylor Series -- 42. Sequences of Holomorphic Functions. Chapter 5: GENERALIZATIONS TO HIGHER DIMENSIONS -- 43. Introduction -- 44. The Spaces Cn -- 45. The Idempotent Representation -- 46. Singular Elements -- Cauchy-Riemann Matrices -- 47. Power Series and Holomorphic Functions in Cn -- 48. Derivatives of Functions in Cn -- 49. Integrals and Their Applications -- Chapter 6: EPILOGUE -- BIBLIOGRAPHY -- INDEX. … (more)
- Publisher Details:
- Abingdon : Routledge
- Publication Date:
- 2018
- Copyright Date:
- 1991
- Extent:
- 1 online resource
- Subjects:
- 512.55
Banach algebras
Holomorphic functions
Electronic books - Languages:
- English
- ISBNs:
- 9781351467087
1351467085 - Notes:
- Note: Includes bibliographical references and index.
- Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
- Access Usage:
- Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.284878
- Ingest File:
- 02_327.xml