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
Construction de p-multiplicateurs
Using characteristic functions of polyhedra, we construct radial p-multipliers which are continuous over but not continuously differentiable through and give a p-multiplier criterion for homogeneous functions over . We also exhibit fractal p-multipliers over the real line.
Construction of almost periodic functions with given properties.
Construction of almost periodic sequences with given properties.
Construction of functions with prescribed Hölder and chirp exponents.
We show that the Hölder exponent and the chirp exponent of a function can be prescribed simultaneously on a set of full measure, if they are both lower limits of continuous functions. We also show that this result is optimal: In general, Hölder and chirp exponents cannot be prescribed outside a set of Hausdorff dimension less than one. The direct part of the proof consists in an explicit construction of a function determined by its orthonormal wavelet coefficients; the optimality is the direct consequence...
Construction of non separable dyadic compactly supported orthonormal wavelet bases for L2(R2) of arbitrarily high regularity.
By means of simple computations, we construct new classes of non separable QMF's. Some of these QMF's will lead to non separable dyadic compactly supported orthonormal wavelet bases for L2(R2) of arbitrarily high regularity.
Construction of Non-MSF Non-MRA Wavelets for L²(ℝ) and H²(ℝ) from MSF Wavelets
Considering symmetric wavelet sets consisting of four intervals, a class of non-MSF non-MRA wavelets for L²(ℝ) and dilation 2 is obtained. In addition, we obtain a family of non-MSF non-MRA H²-wavelets which includes the one given by Behera [Bull. Polish Acad. Sci. Math. 52 (2004), 169-178].
Constructions de bases orthonormées d'ondelettes.
Constructive function theory and spline systems
Continous Wavelet Transforms with Applications to Analyzing Functions on Spheres.
Continuite-Besov des operateurs definis par des integrales singulieres.