Preface.- History of Quaternion and Clifford-Fourier Transforms and Wavelets
Part I: Quaternions.- 1 Quaternion Fourier Transform: Re-tooling Image and Signal Processing Analysis.- 2 The Orthogonal 2D Planes Split of Quaternions and Steerable Quaternion Fourier Transformations.- 3 Quaternionic Spectral Analysis of Non-Stationary Improper Complex Signals.- 4 Quaternionic Local Phase for Low-level Image Processing Using Atomic Functions.- 5 Bochner’s Theorems in the Framework of Quaternion Analysis.- 6 Bochner-Minlos Theorem and Quaternion Fourier Transform
Part II: Clifford Algebra.- 7 Square Roots of -1 in Real Clifford Algebras.- 8 A General Geometric Fourier Transform.- 9 Clifford-Fourier Transform and Spinor Representation of Images
10 Analytic Video (2D+t) Signals Using Clifford-Fourier Transforms in Multiquaternion Grassmann-Hamilton-Clifford Algebras
11 Generalized Analytic Signals in Image Processing: Comparison, Theory and Applications
12 Color Extension of Monogenic Wavelets with Geometric Algebra: Application to Color Image Denoising
13 Seeing the Invisible and Maxwell’s Equations
14 A Generalized Windowed Fourier Transform in Real Clifford Algebra Cl_{0,n}
15 The Balian-Low theorem for the Windowed Clifford-Fourier Transform
16 Sparse Representation of Signals in Hardy Space. - Index
Preface.- History of Quaternion and Clifford-Fourier Transforms and Wavelets
Part I: Quaternions.- 1 Quaternion Fourier Transform: Re-tooling Image and Signal Processing Analysis.- 2 The Orthogonal 2D Planes Split of Quaternions and Steerable Quaternion Fourier Transformations.- 3 Quaternionic Spectral Analysis of Non-Stationary Improper Complex Signals.- 4 Quaternionic Local Phase for Low-level Image Processing Using Atomic Functions.- 5 Bochner’s Theorems in the Framework of Quaternion Analysis.- 6 Bochner-Minlos Theorem and Quaternion Fourier Transform
Part II: Clifford Algebra.- 7 Square Roots of -1 in Real Clifford Algebras.- 8 A General Geometric Fourier Transform.- 9 Clifford-Fourier Transform and Spinor Representation of Images
M.Yu. Kokurin and A. Bakushinsky, Interatively regularized Gauss-Newton methods under random noise
L. Beilina, N.T. Thanh, M.V. Klibanov, and J.B. Malmberg, Methods of quantitative reconstruction of shapes and refractive indices from experimental data
J.B. Malmberg, A posteriori error estimate in the Lagrangian setting for an inverse problem based on a new formulation of Maxwell's system
E. Karchevskii, A. Spiridonov, and L. Beilina, Determination of permittivity from propagation constant measurements in optical fibers
L. Angermann, Yu.V. Shestopalov, and V.V. Yatsyk, Eigenmodes of linearised problems of scattering and generation of oscillations on cubically polarisable layers
S. Soltani, R. Andersson, and B. Andersson, Time resolution in transient kinetics
L. Beilina and A. Eriksson, Reconstruction of dielectric constants in a cylindrical waveguide
L. Beilina and I. Gainova, Time-adaptive FEM for distributed parameter identification in mathematical model of HIV infection with drug therapy
L. Beilina and E. Karchevskii, The layer-stripping algorithm for reconstruction of dielectrics in an optical fiber
L. Beilina, M. Cristofol, and K. Niinimaki, Simultaneous reconstruction of Maxwell's coefficients from backscattering data
M.Yu. Kokurin and A. Bakushinsky, Interatively regularized Gauss-Newton methods under random noise
L. Beilina, N.T. Thanh, M.V. Klibanov, and J.B. Malmberg, Methods of quantitative reconstruction of shapes and refractive indices from experimental data
J.B. Malmberg, A posteriori error estimate in the Lagrangian setting for an inverse problem based on a new formulation of Maxwell's system
V. Abramov, Weil algebra, 3-Lie algebra and B.R.S. algebra
V. Abramov, R. Kerner, and O. Liivapuu, Algebras with ternary composition law combining Z2 and Z3 gradings
V. Abramov and P. Lätt, Ternary Lie Superalgebras and Nambu-Hamilton Equation in Superspace
A. Ben Abdeljelil, M. Elhamdadi, I. Kaygorodov, and A. Makhlouf, Generalized Derivations of n-BiHom-Lie algebras
A. Kitouni, A. Makhlouf and S. Silvestrov, On n-ary generalization of BiHom-Lie algebras and BiHomassociative algebras
A. Kitouni, A. Makhlouf and S. Silvestrov, On solvability and nilpotency for (n+1)-Hom-Lie algebras induced by n-Hom-Lie algebras
I. Bakayoko and S. Silvestrov, Multiplicative n-Hom-Lie color algebras
A. Makhlouf and M. Mehidi, On classification of Filiform Hom-Lie algebras
E. Ongong’a, Johan Richter, and S. Silvestrov, Classification of low-dimensional Hom-Lie algebras
A. Armakan and S. Silvestrov, Enveloping algebras of certain types of color hom-Lie algebras
S. K. Mishra and S. Silvestrov, A Review on Hom-Gerstenhaber algebras and Hom-Lie algebroids
L. Hellström, Strong Hom-associativity
Tianshui Ma, S. Silvestrov, and H. Zheng, On Hom-Yetter-Drinfeld category
I. R. Churchill, M. Elhamdadi and N. Van Kempen, On the classification of f - quandles
P. Nystedt, Noncommutatively graded algebras
A. Dimakis and F. Müller-Hoissen, Differential Calculi on Associative Algebras and Integrable Systems
V. V. Bavula, The Jacobian Conjecture2 n implies the Dixmier Problem n
A. B. Tumwesigye, J. Richter, S. Silvestrov, Commutants in crossed product algebras for piecewise constant functions on the real line
A. B. Tumwesigye, J. Richter, S. Silvestrov, Ore extensions of functional algebras
A. B. Tumwesigye, J. Richter, S. Silvestrov, Centralizers in PBW Extensions
J. Musonda, S. Kaijser, and S. Silvestrov, Reordering, centralizers and centers in an algebra with three generators and Lie type relations
J. Musonda, J. Richter, and S. Silvestrov, Reordering in noncommutative algebras associated with iterated function systems
J. Musonda, J. Richter, and S. Silvestrov, Twisted difference operator representations of deformed Lie type commutation relations
R. R. Cantuba and S. Silvestrov, Torsion-type q-deformed Heisenberg algebra and its Lie polynomials
R. R. Cantuba, S. Silvestrov, Lie polynomial characterization problems
S. Silvestrov, P. M. Rajkovic, S. D. Marinkovic, and M. S. Stankovic
Relations Between the Fractional Operators in q–Calculus
T. Ernst, On the exponential and trigonometric q;w-special functions
M. Mitrovic and S. Silvestrov, Isomorphism theorems for basic constructive algebraic structures with special emphasize on constructive semigroups with apartness -an overview
M. Mitrovic and S. Silvestrov, Semilatice decompositions of semigroups. Hereditariness and periodicity – an overview
T. Nazir and S. Silvestrov, Common Fixed Point for Integral Type Contractive Mappings in Multiplicative Metric Spaces
T. Nazir and S. Silvestrov, Cyclic Contractions and Common Fixed Point Results of Integral Type Contractions in Multiplicative Metric Spaces
K. Lundengård, J. Österberg, S. Silvestrov, Extreme points of the Vandermonde determinant on the sphere and some limits involving the generalized Vandermonde determinant
A. K. Muhumuza, K. Lundengård, J. Österberg, S. Silvestrov, J. M. Mango and G. Kakuba, Extreme Points of the Vandermonde Determinant on Surfaces Implicitly Determined by a Univariate Polynomial
A. K. Muhumuza, K. Lundengård, J. Österberg, S. Silvestrov, J. M. Mango, and G. Kakuba, Optimization of the Wishart joint eigenvalue probability density distribution based on the Vandermonde determinant
A. Malyarenko, H. Nohrouzian, and S. Silvestrov, An algebraic method for pricing financial instruments on post-crisis market
B. Canhanga, A. Malyarenko, J.-P. Murara, Y. Ni and S. Silvestrov, Advanced Monte Carlo pricing of European options in a market model with two stochastic volatilities
C. Nhangumbe, E. Fredericks and B. Canhanga, Lie Symmetry Analysis on Pricing Weather Derivatives by Partial Differential Equations
D. Silvestrov, S. Silvestrov, B. Abola, P. S. Biganda, C. Engström, J. M. Mango and G. Kakuba, Perturbation analysis for stationary distributions of Markov chains with damping component
M. Dogan, Uniqueness of p-adic Gibbs measures for p-adic l-Ising model on Cayley Tree of arbitrary order
I. Chandarki and B. Singh, On Pade Approximants Series Solutions of MHD Flow Equations with Heat and Mass Transfer Due to a Point Sink
Index
V. Abramov, Weil algebra, 3-Lie algebra and B.R.S. algebra
V. Abramov, R. Kerner, and O. Liivapuu, Algebras with ternary composition law combining Z2 and Z3 gradings
V. Abramov and P. Lätt, Ternary Lie Superalgebras and Nambu-Hamilton Equation in Superspace