Eckhard Hitzer
Quaternion and Clifford Fourier Transforms
Eckhard Hitzer
Quaternion and Clifford Fourier Transforms
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This book describes the development of quaternion and Clifford Fourier transforms in Clifford (geometric) algebra over the last 30 years. It is the first comprehensive self-contained book covering this vibrant new area of pure and applied mathematics in depth.
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This book describes the development of quaternion and Clifford Fourier transforms in Clifford (geometric) algebra over the last 30 years. It is the first comprehensive self-contained book covering this vibrant new area of pure and applied mathematics in depth.
Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Produktdetails
- Produktdetails
- Verlag: Taylor & Francis Ltd
- Seitenzahl: 476
- Erscheinungstermin: 25. September 2023
- Englisch
- Abmessung: 254mm x 178mm x 25mm
- Gewicht: 884g
- ISBN-13: 9781032026589
- ISBN-10: 1032026588
- Artikelnr.: 68714258
- Herstellerkennzeichnung
- Books on Demand GmbH
- In de Tarpen 42
- 22848 Norderstedt
- info@bod.de
- 040 53433511
- Verlag: Taylor & Francis Ltd
- Seitenzahl: 476
- Erscheinungstermin: 25. September 2023
- Englisch
- Abmessung: 254mm x 178mm x 25mm
- Gewicht: 884g
- ISBN-13: 9781032026589
- ISBN-10: 1032026588
- Artikelnr.: 68714258
- Herstellerkennzeichnung
- Books on Demand GmbH
- In de Tarpen 42
- 22848 Norderstedt
- info@bod.de
- 040 53433511
Eckhard Hitzer has a PhD in theoretical physics from the University of Konstanz (Germany). He has been living in Japan since 1996 (Kyoto University, University of Fukui, and since 2012 as Senior Associate Professor at International Christian University [ICU] in Mitaka, Tokyo). He teaches Physics and Mathematics at ICU. He has published over 100 International Scientific journal papers and book chapters, is member of the editorial boards of three journals, author of one book, editor of two books and of 10 special journal issues and conference proceedings, active member and organizer of many scientific conference committees and prize committees. He edits the Email newsletter for everyone interested in Clifford Algebra and Geometric Algebra (GA-Net) since 2003, and the blog GA-Net Updates since 2012. He works on pure and applied Clifford (geometric) algebras, with specialization on space group symmetry in crystallography, neural network and artificial intelligence applications, and Clifford algebra based integral transformations. He has been co-organizing the session Quaternion and Clifford Fourier Transforms and Wavelets at the tri-annual International Conferences on Clifford Algebras and their Applications since past ten years, and the annual workshop Empowering Novel Geometric Algebra for Graphics & Engineering (ENGAGE) at the international conference Computer Graphics International (CGI) since past five years.
1. Introduction. 1.1. Brief Historical Notes. 1.2. Quaternion Fourier
Transforms (QFT). 1.3. Clifford Fourier Transforms in Clifford's Geometric
Algebra. 1.4. Quaternion and Clifford Wavelets. 2. Clifford Algebra. 2.1.
Axioms of Clifford Algebra. 2.2. Quadratic Forms in Clifford's Geometric
Algebra. 2.3. Clifford Product and Derived Products. 2.4. Determinants in
Geometric Algebra. 2.5. Gram-Schmidt Orthogonalization in Geometric
Algebra. 2.6. Important Clifford Geometric Algebras. 2.7. How Imaginary
Numbers Become Real in Clifford Algebras. 2.8. Quaternions and Geometry of
Rotations In 3, 4 Dim. 3. Geometric Calculus. 3.1. Introductory Notes on
Vector Differential Calculus. 3.2. Brief Overview of Vector Differential
Calculus. 3.3. Geometric Algebra for Differential Calculus. 3.4. Vector
Differential Calculus. 3.5. Summary on Vector Differential Calculus. 4.
Quaternion Fourier Transforms. 4.1. Fundamentals of Quaternion Fourier
Transforms (QFT). 4.2. Properties of Quaternion Fourier Transform. 4.3.
Special Quaternion Fourier Transforms. 4.4. From QFT To Volume-Time FT,
Spacetime FT. 5. Clifford Fourier Transforms. 5.1. Overview of Clifford
Fourier Transforms. 5.2. One-Sided Clifford Fourier Transforms. 5.3.
Two-Sided Clifford Fourier Transforms. 5.4. Clifford Fourier Transform and
Convolution. 5.5. Special Clifford Fourier Transforms. 6. Relating QFTs And
CFTs. 6.1. Background. 6.2. General Geometric Fourier Transform. 6.3. CFT
Due to Sommen And Bülow. 6.4. Color Image CFT. 6.5. Two-Sided CFT. 6.6.
Quaternion Fourier Transform (QFT) 6.7. Quaternion Fourier Stieltjes
Transform. 6.8. Quaternion Fourier Mellin Transform, Clifford Fourier
Mellin Transform. 6.9. Volume-Time CFT and Spacetime CFT. 6.10. One-Sided
CFTs. 6.11. Pseudoscalar Kernel CFTs. 6.12. Quaternion and Clifford Linear
Canonical Transforms. 6.13. Summary Interrelationship Of QFTs, CFTs.
Appendix A. Square Roots of ¿1 MAPLE, Cauchy-Schwarz, Uncertainty Equality.
References. Bibliography. Index.
Transforms (QFT). 1.3. Clifford Fourier Transforms in Clifford's Geometric
Algebra. 1.4. Quaternion and Clifford Wavelets. 2. Clifford Algebra. 2.1.
Axioms of Clifford Algebra. 2.2. Quadratic Forms in Clifford's Geometric
Algebra. 2.3. Clifford Product and Derived Products. 2.4. Determinants in
Geometric Algebra. 2.5. Gram-Schmidt Orthogonalization in Geometric
Algebra. 2.6. Important Clifford Geometric Algebras. 2.7. How Imaginary
Numbers Become Real in Clifford Algebras. 2.8. Quaternions and Geometry of
Rotations In 3, 4 Dim. 3. Geometric Calculus. 3.1. Introductory Notes on
Vector Differential Calculus. 3.2. Brief Overview of Vector Differential
Calculus. 3.3. Geometric Algebra for Differential Calculus. 3.4. Vector
Differential Calculus. 3.5. Summary on Vector Differential Calculus. 4.
Quaternion Fourier Transforms. 4.1. Fundamentals of Quaternion Fourier
Transforms (QFT). 4.2. Properties of Quaternion Fourier Transform. 4.3.
Special Quaternion Fourier Transforms. 4.4. From QFT To Volume-Time FT,
Spacetime FT. 5. Clifford Fourier Transforms. 5.1. Overview of Clifford
Fourier Transforms. 5.2. One-Sided Clifford Fourier Transforms. 5.3.
Two-Sided Clifford Fourier Transforms. 5.4. Clifford Fourier Transform and
Convolution. 5.5. Special Clifford Fourier Transforms. 6. Relating QFTs And
CFTs. 6.1. Background. 6.2. General Geometric Fourier Transform. 6.3. CFT
Due to Sommen And Bülow. 6.4. Color Image CFT. 6.5. Two-Sided CFT. 6.6.
Quaternion Fourier Transform (QFT) 6.7. Quaternion Fourier Stieltjes
Transform. 6.8. Quaternion Fourier Mellin Transform, Clifford Fourier
Mellin Transform. 6.9. Volume-Time CFT and Spacetime CFT. 6.10. One-Sided
CFTs. 6.11. Pseudoscalar Kernel CFTs. 6.12. Quaternion and Clifford Linear
Canonical Transforms. 6.13. Summary Interrelationship Of QFTs, CFTs.
Appendix A. Square Roots of ¿1 MAPLE, Cauchy-Schwarz, Uncertainty Equality.
References. Bibliography. Index.
1. Introduction. 1.1. Brief Historical Notes. 1.2. Quaternion Fourier
Transforms (QFT). 1.3. Clifford Fourier Transforms in Clifford's Geometric
Algebra. 1.4. Quaternion and Clifford Wavelets. 2. Clifford Algebra. 2.1.
Axioms of Clifford Algebra. 2.2. Quadratic Forms in Clifford's Geometric
Algebra. 2.3. Clifford Product and Derived Products. 2.4. Determinants in
Geometric Algebra. 2.5. Gram-Schmidt Orthogonalization in Geometric
Algebra. 2.6. Important Clifford Geometric Algebras. 2.7. How Imaginary
Numbers Become Real in Clifford Algebras. 2.8. Quaternions and Geometry of
Rotations In 3, 4 Dim. 3. Geometric Calculus. 3.1. Introductory Notes on
Vector Differential Calculus. 3.2. Brief Overview of Vector Differential
Calculus. 3.3. Geometric Algebra for Differential Calculus. 3.4. Vector
Differential Calculus. 3.5. Summary on Vector Differential Calculus. 4.
Quaternion Fourier Transforms. 4.1. Fundamentals of Quaternion Fourier
Transforms (QFT). 4.2. Properties of Quaternion Fourier Transform. 4.3.
Special Quaternion Fourier Transforms. 4.4. From QFT To Volume-Time FT,
Spacetime FT. 5. Clifford Fourier Transforms. 5.1. Overview of Clifford
Fourier Transforms. 5.2. One-Sided Clifford Fourier Transforms. 5.3.
Two-Sided Clifford Fourier Transforms. 5.4. Clifford Fourier Transform and
Convolution. 5.5. Special Clifford Fourier Transforms. 6. Relating QFTs And
CFTs. 6.1. Background. 6.2. General Geometric Fourier Transform. 6.3. CFT
Due to Sommen And Bülow. 6.4. Color Image CFT. 6.5. Two-Sided CFT. 6.6.
Quaternion Fourier Transform (QFT) 6.7. Quaternion Fourier Stieltjes
Transform. 6.8. Quaternion Fourier Mellin Transform, Clifford Fourier
Mellin Transform. 6.9. Volume-Time CFT and Spacetime CFT. 6.10. One-Sided
CFTs. 6.11. Pseudoscalar Kernel CFTs. 6.12. Quaternion and Clifford Linear
Canonical Transforms. 6.13. Summary Interrelationship Of QFTs, CFTs.
Appendix A. Square Roots of ¿1 MAPLE, Cauchy-Schwarz, Uncertainty Equality.
References. Bibliography. Index.
Transforms (QFT). 1.3. Clifford Fourier Transforms in Clifford's Geometric
Algebra. 1.4. Quaternion and Clifford Wavelets. 2. Clifford Algebra. 2.1.
Axioms of Clifford Algebra. 2.2. Quadratic Forms in Clifford's Geometric
Algebra. 2.3. Clifford Product and Derived Products. 2.4. Determinants in
Geometric Algebra. 2.5. Gram-Schmidt Orthogonalization in Geometric
Algebra. 2.6. Important Clifford Geometric Algebras. 2.7. How Imaginary
Numbers Become Real in Clifford Algebras. 2.8. Quaternions and Geometry of
Rotations In 3, 4 Dim. 3. Geometric Calculus. 3.1. Introductory Notes on
Vector Differential Calculus. 3.2. Brief Overview of Vector Differential
Calculus. 3.3. Geometric Algebra for Differential Calculus. 3.4. Vector
Differential Calculus. 3.5. Summary on Vector Differential Calculus. 4.
Quaternion Fourier Transforms. 4.1. Fundamentals of Quaternion Fourier
Transforms (QFT). 4.2. Properties of Quaternion Fourier Transform. 4.3.
Special Quaternion Fourier Transforms. 4.4. From QFT To Volume-Time FT,
Spacetime FT. 5. Clifford Fourier Transforms. 5.1. Overview of Clifford
Fourier Transforms. 5.2. One-Sided Clifford Fourier Transforms. 5.3.
Two-Sided Clifford Fourier Transforms. 5.4. Clifford Fourier Transform and
Convolution. 5.5. Special Clifford Fourier Transforms. 6. Relating QFTs And
CFTs. 6.1. Background. 6.2. General Geometric Fourier Transform. 6.3. CFT
Due to Sommen And Bülow. 6.4. Color Image CFT. 6.5. Two-Sided CFT. 6.6.
Quaternion Fourier Transform (QFT) 6.7. Quaternion Fourier Stieltjes
Transform. 6.8. Quaternion Fourier Mellin Transform, Clifford Fourier
Mellin Transform. 6.9. Volume-Time CFT and Spacetime CFT. 6.10. One-Sided
CFTs. 6.11. Pseudoscalar Kernel CFTs. 6.12. Quaternion and Clifford Linear
Canonical Transforms. 6.13. Summary Interrelationship Of QFTs, CFTs.
Appendix A. Square Roots of ¿1 MAPLE, Cauchy-Schwarz, Uncertainty Equality.
References. Bibliography. Index.