Gabor Frames, Unimodularity, and Window Decay.
Gabor meets Littlewood-Paley: Gabor expansions in
It is known that Gabor expansions do not converge unconditionally in and that cannot be characterized in terms of the magnitudes of Gabor coefficients. By using a combination of Littlewood-Paley and Gabor theory, we show that can nevertheless be characterized in terms of Gabor expansions, and that the partial sums of Gabor expansions converge in -norm.
Gaussian quadrature for matrix valued functions on the unit circle.
G-continuous frames and coorbit spaces.
Gegenbauer polynomials and semiseparable matrices.
General Discrepancy Estimates III: The Erdös-Turán-Koksma Inequality for the Haar Function System.
General Franklin systems as bases in H¹[0,1]
By a general Franklin system corresponding to a dense sequence of knots 𝓣 = (tₙ, n ≥ 0) in [0,1] we mean a sequence of orthonormal piecewise linear functions with knots 𝓣, that is, the nth function of the system has knots t₀, ..., tₙ. The main result of this paper is a characterization of sequences 𝓣 for which the corresponding general Franklin system is a basis or an unconditional basis in H¹[0,1].
Generalisations of some properties of invariant polynomials with matrix arguments
Some extensions of the properties of invariant polynomials proved by Davis (1980), Chikuse (1980), Chikuse and Davis (1986) and Ratnarajah et al. (2005) are given for symmetric and Hermitian matrices.
Generalized absolute convergence of single and double Vilenkin-Fourier series and related results
We consider the Vilenkin orthonormal system on a Vilenkin group and the Vilenkin-Fourier coefficients , , of functions for some . We obtain certain sufficient conditions for the finiteness of the series , where is a given sequence of positive real numbers satisfying a mild assumption and . We also find analogous conditions for the double Vilenkin-Fourier series. These sufficient conditions are in terms of (either global or local) moduli of continuity of and give multiplicative analogue...
Generalized atomic subspaces for operators in Hilbert spaces
We introduce the notion of a -atomic subspace for a bounded linear operator and construct several useful resolutions of the identity operator on a Hilbert space using the theory of -fusion frames. Also, we shall describe the concept of frame operator for a pair of -fusion Bessel sequences and some of their properties.
Generalized Calderón conditions and regular orbit spaces
The construction of generalized continuous wavelet transforms on locally compact abelian groups A from quasi-regular representations of a semidirect product group G = A ⋊ H acting on L²(A) requires the existence of a square-integrable function whose Plancherel transform satisfies a Calderón-type resolution of the identity. The question then arises under what conditions such square-integrable functions exist. The existing literature on this subject leaves a gap between sufficient and necessary criteria....
Generalized conjugate systems on local fields
Generalized Fourier expansions for distributions and ultradistributions.
Generalized Multi-Resolution Analyses and a Construction Procedure for All Wavelet Sets in ...
Generalized Riesz products produced from orthonormal transforms
Let be a finite set of step functions or real valued trigonometric polynomials on = [0,1) satisfying a certain orthonormality condition. We study multiscale generalized Riesz product measures μ defined as weak-* limits of elements , where are -dimensional subspaces of L₂() spanned by an orthonormal set which is produced from dilations and multiplications of elements of and . The results involve mutual absolute continuity or singularity of such Riesz products extending previous results on...
Generalized Rudin-Shapiro Systems.
Generalized Schauder frames
Schauder frames were introduced by Han and Larson [9] and further studied by Casazza, Dilworth, Odell, Schlumprecht and Zsak [2]. In this paper, we have introduced approximative Schauder frames as a generalization of Schauder frames and a characterization for approximative Schauder frames in Banach spaces in terms of sequence of non-zero endomorphism of finite rank has been given. Further, weak* and weak approximative Schauder frames in Banach spaces have been defined. Finally, it has been proved...
Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials: a survey.
Generating new classes of orthogonal polynomials.
Generating some semiclassical orthogonal polynomials.