Describing Functions: Atomic Decompositions Versus Frames.
Designing Multiresolution Analysis-type Wavelets and Their Fast Algorithms.
Determination of the number of texture segments using wavelets.
Developments from nonharmonic Fourier series.
Diagonals of Self-adjoint Operators with Finite Spectrum
Given a finite set X⊆ ℝ we characterize the diagonals of self-adjoint operators with spectrum X. Our result extends the Schur-Horn theorem from a finite-dimensional setting to an infinite-dimensional Hilbert space analogous to Kadison's theorem for orthogonal projections (2002) and the second author's result for operators with three-point spectrum (2013).
Differential operators and spectral distributions of invariant ensembles from the classical orthogonal polynomials: the discrete case.
Differentiation and the Balian-Low Theorem.
Digital Nets and Sequences Constructed over Finite Rings and Their Application to Quasi-Monte Carlo Integration.
Dimension functions, scaling sequences, and wavelet sets
The paper is a continuation of our study of dimension functions of orthonormal wavelets on the real line with dyadic dilations. The main result of Section 2 is Theorem 2.8 which provides an explicit reconstruction of the underlying generalized multiresolution analysis for any MSF wavelet. In Section 3 we reobtain a result of Bownik, Rzeszotnik and Speegle which states that for each dimension function D there exists an MSF wavelet whose dimension function coincides with D. Our method provides a completely...
Discrepancy and integration in function spaces with dominating mixed smoothness [Book]
Discrete differential operators in multidimensional Haar wavelet spaces.
Discrete Laguerre functions and equilibrium conditions.
Discrete orthogonality of Zernike functions.
Divergence of general operators on sets of measure zero
We consider sequences of linear operators Uₙ with a localization property. It is proved that for any set E of measure zero there exists a set G for which diverges at each point x ∈ E. This result is a generalization of analogous theorems known for the Fourier sum operators with respect to different orthogonal systems.
Divergent Cesàro means of Jacobi-Sobolev expansions.
Dos sistemas adicionales de polinomios relacionados con los polinomios de Pollaczek
Double Fourier Series with Coefficients O (n m) -1.
Dual Szegő pairs of sequences of rational matrix-valued functions.
Duality, reflexivity and atomic decompositions in Banach spaces
We study atomic decompositions and their relationship with duality and reflexivity of Banach spaces. To this end, we extend the concepts of "shrinking" and "boundedly complete" Schauder basis to the atomic decomposition framework. This allows us to answer a basic duality question: when an atomic decomposition for a Banach space generates, by duality, an atomic decomposition for its dual space. We also characterize the reflexivity of a Banach space in terms of properties of its atomic decompositions....
Dunkl wavelets and applications to inversion of the Dunkl intertwining operator and its dual.