Characterization of generators for multiresolution analyses with composite dilations.
Characterization of in terms of generalized Littlewood-Paley g-functions
Characterization of low pass filters in a multiresolution analysis
We characterize the low pass filters associated with scaling functions of a multiresolution analysis in a general context, where instead of the dyadic dilation one considers the dilation given by a fixed linear invertible map A: ℝⁿ → ℝⁿ such that A(ℤⁿ) ⊂ ℤⁿ and all (complex) eigenvalues of A have modulus greater than 1. This characterization involves the notion of filter multiplier of such a multiresolution analysis. Moreover, the paper contains a characterization of the measurable functions which...
Characterization of L...(R...) Using Gabor Frames.
Characterization of measures in the group C*-algebra of a locally compact group.
Characterization of moment multisequences by a variation of positive definiteness.
Characterization of rearrangement invariant spaces with fixed points for the Hardy-Littlewood maximal operator.
Characterization of the Besov-Lipschitz and Triebel-Lizorkin Spaces the Case q < 1.
Characterization of the boundedness for a family of commutators on
Characterization of the convolution operators on quasianalytic classes of Beurling type that admit a continuous linear right inverse
Extending previous work by Meise and Vogt, we characterize those convolution operators, defined on the space of (ω)-quasianalytic functions of Beurling type of one variable, which admit a continuous linear right inverse. Also, we characterize those (ω)-ultradifferential operators which admit a continuous linear right inverse on for each compact interval [a,b] and we show that this property is in fact weaker than the existence of a continuous linear right inverse on .
Characterization of the strict convexity of the Besicovitch-Musielak-Orlicz space of almost periodic functions
We introduce the new class of Besicovitch-Musielak-Orlicz almost periodic functions and consider its strict convexity with respect to the Luxemburg norm.
Characterizations of Gabor Systems via the Fourier transform.
We give characterizations of orthogonal families, tight frames and orthonormal bases of Gabor systems. The conditions we propose are stated in terms of equations for the Fourier transforms of the Gabor system's generating functions.
Characterizations of Localized BMO() via Commutators of Localized Riesz Transforms and Fractional Integrals Associated to Schr“odinger Operators and Fractional Integrals Associated to Schr“odinger Operators.
Characterizations of periodic function spaces of Besov-Sobolev type via approximation processes and relations to the strong summability of Fourier series
Characterizations of those Ideals in L1 (R) which can be Synthesized.
Characterizations of tight frame wavelets with special dilation matrices.
Characterizing Sidon sets by interpolation properties of subsets
Pisier's characterization of Sidon sets as containing proportional-sized quasi-independent subsets is given a sharper form for groups with only a finite number of elements having orders a power of 2. No such improvement is possible for a general Sidon subset of a group having an infinite number of elements of order 2. The method used also gives several sharper forms of Ramsey's characterization of Sidon sets as containing proportional-sized I₀-subsets in a uniform way, again in groups containing...
Characterizing translation invariant projections on Sobolev spaces on tori by the coset ring and Paley projections
We characterize those anisotropic Sobolev spaces on tori in the and uniform norms for which the idempotent multipliers have a description in terms of the coset ring of the dual group. These results are deduced from more general theorems concerning invariant projections on vector-valued function spaces on tori. This paper is a continuation of the author’s earlier paper [W].
Charakterisierungen von nirgends differenzierbaren Weierstraß-Funktionen durch Replikativität.
Checkerboards, Lipschitz functions and uniform rectifiability.
In his recent lecture at the International Congress [S], Stephen Semmes stated the following conjecture for which we provide a proof.Theorem. Suppose Ω is a bounded open set in Rn with n > 2, and suppose that B(0,1) ⊂ Ω, Hn-1(∂Ω) = M < ∞ (depending on n and M) and a Lipschitz graph Γ (with constant L) such that Hn-1(Γ ∩ ∂Ω) ≥ ε.Here Hk denotes k-dimensional Hausdorff measure and B(0,1) the unit ball in Rn. By iterating our proof we obtain a slightly stronger result which allows us...