Continuity of Calderón-Zygmund operators on the space BMO.
Continuous -frame in Hilbert -modules.
Control norms for large control times
Control Norms for Large Control Times
A control system of the second order in time with control is considered. If the system is controllable in a strong sense and uT is the control steering the system to the rest at time T, then the L2–norm of uT decreases as while the –norm of uT is approximately constant. The proof is based on the moment approach and properties of the relevant exponential family. Results are applied to the wave equation with boundary or distributed controls.
Convergence of Series of Translations.
Coorbit space theory for quasi-Banach spaces
We generalize the classical coorbit space theory developed by Feichtinger and Gröchenig to quasi-Banach spaces. As a main result we provide atomic decompositions for coorbit spaces defined with respect to quasi-Banach spaces. These atomic decompositions are used to prove fast convergence rates of best n-term approximation schemes. We apply the abstract theory to time-frequency analysis of modulation spaces , 0 < p,q ≤ ∞.
Corrigendum to the paper "Pointwise convergence for expansions in surface harmonics of arbitrary dimension".
Das Verhalten der Greenschen Matrix und der Entwicklungen nach Eigenfunktionen N-regulärer Eigenwertprobleme.
Decay of Fourier transforms and summability of eigenfunction expansions
Decomposition systems for function spaces
Let be a decomposition system for indexed over D, the set of dyadic cubes in , and a finite set E, and let be the corresponding dual functionals. That is, for every , . We study sufficient conditions on Θ,Θ̃ so that they constitute a decomposition system for Triebel-Lizorkin and Besov spaces. Moreover, these conditions allow us to characterize the membership of a distribution f in these spaces by the size of the coefficients , e ∈ E, I ∈ D. Typical examples of such decomposition systems...
Describing Functions: Atomic Decompositions Versus Frames.
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).
Differentiation and the Balian-Low Theorem.
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...
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.
-orbit functions.
Efficient Computation of Fourier Transforms on Compact Groups.
Estimates for spline orthonormal functions and for their derivatives
Expansions for Gaussian processes and Parseval frames.