Compression and restoration of square integrable functions.
Compression of satellite data.
In this paper, we present the simple and double compression algorithms with an error control for compressing satellite data corresponding to several revolutions. The compressions are performed by means of approximations in the norm L∞ by finite series of Chebyshev polynomials, with their known properties of fast evaluation, uniform distribution of the error, and validity over large intervals of time. By using the error control here introduced, the number of terms of the series is given automatically...
Compression on the digital unit sphere.
Computation with wavelets in higher dimensions.
Computer graphics and a new Gibbs phenomenon for Fourier-Bessel series.
Computing discrete convolutions with verified accuracy via Banach algebras and the FFT
We introduce a method to compute rigorous component-wise enclosures of discrete convolutions using the fast Fourier transform, the properties of Banach algebras, and interval arithmetic. The purpose of this new approach is to improve the implementation and the applicability of computer-assisted proofs performed in weighed Banach algebras of Fourier/Chebyshev sequences, whose norms are known to be numerically unstable. We introduce some application examples, in particular a rigorous aposteriori...
Concepts of generalized bounded variation and the theory of Fourier series.
Concerning the order approximation of periodic continuous functions by trigonometric interpolation polynomials II
Conditional Fourier-Feynman transform given infinite dimensional conditioning function on abstract Wiener space
We study a conditional Fourier-Feynman transform (CFFT) of functionals on an abstract Wiener space . An infinite dimensional conditioning function is used to define the CFFT. To do this, we first present a short survey of the conditional Wiener integral concerning the topic of this paper. We then establish evaluation formulas for the conditional Wiener integral on the abstract Wiener space . Using the evaluation formula, we next provide explicit formulas for CFFTs of functionals in the Kallianpur...
Conditions d'entropie assurant la continuité de certains processus et applications à l'analyse harmonique
Confirmation of Matheron's conjecture on the covariogram of a planar convex body
Conjugacy for Fourier-Bessel expansions
We define and investigate the conjugate operator for Fourier-Bessel expansions. Weighted norm and weak type (1,1) inequalities are proved for this operator by using a local version of the Calderón-Zygmund theory, with weights in most cases more general than weights. Also results on Poisson and conjugate Poisson integrals are furnished for the expansions considered. Finally, an alternative conjugate operator is discussed.
Conjugate Characterizations of H1 Dyadic Martingales.
Conjugate kernels and convergence of harmonic singular integrals
Conjugate martingale transforms
Characterizations of H₁, BMO and VMO martingale spaces generated by bounded Vilenkin systems via conjugate martingale transforms are studied.
Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula
Starting from the Rodrigues representation of polynomial solutions of the general hypergeometric-type differential equation complementary polynomials are constructed using a natural method. Among the key results is a generating function in closed form leading to short and transparent derivations of recursion relations and addition theorem. The complementary polynomials satisfy a hypergeometric-type differential equation themselves, have a three-term recursion among others and obey Rodrigues formulas....
Connectivity, homotopy degree, and other properties of α-localized wavelets on R.
In this paper, we study general properties of α-localized wavelets and multiresolution analyses, when 1/2 < α ≤ ∞. Related to the latter, we improve a well-known result of A. Cohen by showing that the correspondence m → φ' = Π1∞ m(2−j ·), between low-pass filters in Hα(T) and Fourier transforms of α-localized scaling functions (in Hα(R)), is actually a homeomorphism of topological spaces. We also show that the space of such filters can be regarded as a connected infinite dimensional manifold,...
Consistency of trigonometric and polynomial regression estimators
The problem of nonparametric regression function estimation is considered using the complete orthonormal system of trigonometric functions or Legendre polynomials , k=0,1,..., for the observation model , i=1,...,n, where the are independent random variables with zero mean value and finite variance, and the observation points , i=1,...,n, form a random sample from a distribution with density . Sufficient and necessary conditions are obtained for consistency in the sense of the errors , ,...
Constant Coefficient Differential Operators with Slowly Spreading Solutions.
Construction de bases orthonormées d'ondelettes