Approximation Theory, Wavelets and Applications: Proceedings of the Nato Asi on Recent Developments in Approximation Theory, Wavelets and Applications, Maratea, Italy, May 16-26, 1994 - Nato Science Series C

Marc Notes: Proceedings of the NATO Advanced Study Institute on Recent Developments in Approximation Theory, Wavelets, and Applications, Maratea, Italy May 16-26, 1994--T.p.verso.; Includes bibliographical references and index.; Published in cooperation with NATO Scientific Affairs Division.. Table of Contents: Preface. A Class of Interpolating Positive Linear Operators: Theoretical and Computational Aspects; G. Allasia. Quasi-Interpolation; E. W. Cheney. Approximation and Interpolation on Spheres; E. W. Cheney. Exploring Covariance, Consistency and Convergence in Pade Approximation Theory; A. Cuyt. Dijkstra's Cyclic Projections Algorithm: the Rate of Convergence; F. Deutsch. Interpolation from a Convex Subset of Hilbert Space: a Survey of Some Recent Results; F. Deutsch. The Angle between Subspaces of a Hilbert Space; F. Deutsch. Neville Elimination and Approximation Theory; M. Gasca, J. M. Pena. Approximation with Weights, the Chebyshev Measure and the Equilibrium Measure; M. V. Golitschek. A One-Parameter Class of B-Splines; Z. F. Kocak, G. M. Phillips. Interpolation on the Triangle and Simplex; S. L. Lee, G. M. Phillips. Knot Removal for Scattered Data; A. le Mehaute. Error Estimates for Approximation by Radial Basic Functions; W. Light, H. Wayne. Wavelets on the Interval; E. Quak, N. Weyrich. Best Approximations and Fixed Point Theorems; S. P. Singh, B. Watson. How to Approximate the Inverse Operator; J. Appell. On Some Averages of Trigonometric Interpolating Operators; M. Campiti, G. Metafune, D. Pallara. On the Zeros Locations of K > 2 Consecutive Orthogonal Polynomials and of their Derivatives; F. Costabile, R. Luceri. Can Irregular Subdivisions Preserve Convexity? S. de Marchi, M. M. Cecchi. On Functions Approximation by Shepart-Type Operators -- a Survey; B. della Vecchia, G. Mastroianni. Wavelet Representation of the Potential Integral Equations; M. Dorobantu. Lyapunov Theorem in Approximation Theory; C. Franchetti. On the Order Monotonicity of the Metric Projection Operator; G. Isac. Pointwise Estimates forMultivariate Interpolation Using Conditionally Positive Definite Functions; J. Levesley. Experiments with a Wavelet Based Image Denoising Method; M. Malfait, D. Roose. Proximity Maps: Some Continuity Results; G. Marino, P. Pietramala. Non-Smooth Wavelets: Graphing Functions Unbounded in Every Interval; D. L. Ragozin, A. Bruce, H.-Y. Gao. On the Possible Wavelet Packets Orthonormal Bases; S. Saliani. A Case Study in Multivariate Lagrange Interpolation; T. Sauer, Y. Xu. Trigonometric Wavelets for Time-Frequency-Analysis; K. Selig. Interpolating Subspaces in Rn; B. Shekhtman. Multivariate Periodic Interpolating Wavelets; F. Sprengel. Finite Element Multiwavelets; V. Strela, G. Strang. Polynomial Wavelets on [-1,1]; M. Tasche. On the Solution of Discretely Given Fredholm Integral Equations over Lines; E. Venturino. De-Noising Using Wavelets and Cross Validation; N. Weyrich, G. T. Warhola. On the Construction of Two Dimensional Spatial Varying FIR Filter Banks with Perfect Reconstruction; X. Xia, B. W. Suter. Recursions for Tchebycheff B-Splines and their Jumps; Y. Xu. Quasi-Interpolation on Compact Domains; J. Levesley, M. Roach. Index."Publisher Marketing: This text draws together the latest developments in the subject, provides directions for future research, and paves the way for collaborative research. The main topics covered include constructive multivariate approximation, theory of splines, spline wavelets, polynomial and trigonometric wavelets, interpolation theory, polynomial and rational approximation. Among the scientific applications were de-noising using wavelets, including the de-noising of speech and images, and signal and digital image processing. In the area of the approximation of functions the main topics include multivariate interpolation, quasi-interpolation, polynomial approximation with weights, knot removal for scattered data, convergence theorems in Pade theory, Lyapunov theory in approximation, Neville elimination as applied to shape preserving presentation of curves, interpolating positive linear operators, interpolation from a convex subset of Hilbert space and interpolation on the triangle and simplex.

Contributor Bio:  North Atlantic Treaty Organization Dedication. Preface. Acknowledgments. Clifford Geometric Algebras in Multilinear Algebra and Non-Euclidean Geometries.- Geometric algebra Projective Geometries; Affine and other geometries; Affine Geometry of pseudo-euclidean space; Conformal Geometry and the Horosphere; References. Content-Based Information Retrieval by Group Theoretical Methods.- Introduction; Motivating Examples; General Concept; Fault Tolerance.- Applications, Prototypes, and Test Results; Related Work and Future Research; References.- Four Problems in Radar.-Introduction; Radar Fundamentals; Radar Waveforms; Signal Processing; Space-Time Adaptive Processing; Four Problems in Radar; Conclusions. Introduction to Generalized Classical and Quantum Signal and System Theories on Groups and Hypergroups.-Generalized classical signal/system theory on hypergroups; Generalized quantum signal/system theory on hypergroups; Conclusion; References. Lie Groups and Lie Algebras in Robotics.- Introduction -- Rigid Body Motions; Lie Groups; Finite Screw Motions; Mechanical Joints; Invisible Motion and Gripping; Forward Kinematics; Lie Algebra; The Adjoint Representation; The Exponential Map Derivatives of Exponentials; Jacobians; Concluding Remarks; References. Quantum/Classical Interface: a Geometric Approach from the Classical Side.- Introduction Paravector Space as Spacetime; Eigenspinors; Spin; Dirac Equation; Bell's Theorem; Qubits and Entanglement; Conclusions; References. PONS, Reed-Muller Codes, and Group Algebras.- Introduction; Analytic Theory of One-Dimensional PONS (Welti); Shapiro Sequences, Reed-Muller Codes, and Functional Equations; Group Algebras; Reformulation of Classical PONS; Group Algebra of Classical PONS; GroupAlgebra Convolution; Splitting Sequences; Historical Appendix on PONS; References. Clifford Algebras as a Unified Language.- Introduction; Clifford algebras as models of physical spaces; Clifford Algebras as Models of Perceptual Multicolor Spaces; Hypercomplex-Valued invariants of nD multicolor images; Conclusions; Acknowledgments; References. Recent Progress and Applications in Group FFTs.-Introduction; Finite group FFTs; FFTs for compact groups; Noncompact groups; References. Group Filters and Image Processing.- Introduction: Classical Digital Signal Processing; Abelian Group DSP; Nonabelian Groups; Examples; Group Transforms; Group Filters; Line-like Images; Acknowledgments; References. A Geometric Algebra Approach to Some Problems of Robot Vision.- Introduction; Local Analysis of Multi-dimensional Signals; Knowledge Based Neural Computing; Acknowledgments; References. Group Theory in Radar and Signal Processing.- Introduction; How a Radar Works; Representations; Representations and Radar; Ambiguity Functions; The Wide Band Case; References. Geometry of Paravector Space with Applications to Relativistic Physics.- Clifford Algebras in Physics; Paravector Space as Spacetime; Interpretation; Eigenspinors; Maxwell's Equation; Conclusions; References. A Unified Approach to Fourier-Clifford-Prometheus Transforms- Introduction; New construction of classical and multiparametric Prometheus transforms; PONS associated with Abelian groups; Fast Fourier-Prometheus Transforms; Conclusions; Acknowledgments; References. Fast Color Wavelet Transforms.- Introduction; Color images; Color Wavelet-Haar-Prometheus transforms; Edge detection and compression of color images; Conclusion; Acknowledgments; References. Selected Problems; Various Authors.- Transformations of Euclidean Space and Clifford Geometric; Algebra; References; On the Distribution of Kloosterman Sums on Polynomials over Quaternions; References; Harmonic Sliding Analysis Problems; References; Spectral Analysis under Conditions of Uncertainty; A Canonical Basis for Maximal Tori of the Reductive Centrizer of a Nilpotent Element; References; 6 The Quantum Chaos Conjecture References; Four Problems in Radar; Topic Index; Author Index