Explicit bounds of complex exponential frames.
Fonctions a support compact dans les analyses multi-résolutions.
The main topic of this paper is the study of compactly supported functions in a multi-resolution analysis and especially of the minimally supported ones. We will show that this class of functions is stable under differentiation and integration and how to compute basic quantities with them.
Fractal multiwavelets related to the Cantor dyadic group.
Frame characterizations of Besov and Triebel-Lizorkin spaces on spaces of homogeneous type and their applications.
Frame functions and completeness of inner product spaces
Frames for Fréchet spaces
From Continous to Discrete Weyl-Heisenberg Frames Through Sampling.
From the Original Framer to Present-Day Time-Frequency and Time-Scale Frames.
G-continuous frames and coorbit spaces.
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 Fourier expansions for distributions and ultradistributions.
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...
Haar wavelets on the Lebesgue spaces of local fields of positive characteristic
We construct the Haar wavelets on a local field K of positive characteristic and show that the Haar wavelet system forms an unconditional basis for , 1 < p < ∞. We also prove that this system, normalized in , is a democratic basis of . This also proves that the Haar system is a greedy basis of for 1 < p < ∞.
Hermite and Laguerre wave packet expansions
This paper describes expansions in terms of Hermite and Laguerre functions similar to the Frazier-Jawerth expansion in Fourier analysis. The wave packets occurring in these expansions are finite linear combinations of Hermite and Laguerre functions. The Shannon sampling formula played an important role in the derivation of the Frazier-Jawerth expansion. In this paper we use the Christoffel-Darboux formula for orthogonal polynomials instead. We obtain estimates on the decay of the Hermite and Laguerre...
Hermite expansions on R2n for radial functions.
Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms.
We extend an uncertainty principle due to Beurling into a characterization of Hermite functions. More precisely, all functions f on Rd which may be written as P(x)exp(-(Ax,x)), with A a real symmetric definite positive matrix, are characterized by integrability conditions on the product f(x)f(y). We then obtain similar results for the windowed Fourier transform (also known, up to elementary changes of functions, as the radar ambiguity function or the Wigner transform). We complete the paper with...
Improved Sobolev embedding theorem
Infinite matrices, wavelet coefficients and frames.
Ingham type theorems and applications to control theory
Ingham [6] ha migliorato un risultato precedente di Wiener [23] sulle serie di Fourier non armoniche. Modificando la sua funzione di peso noi otteniamo risultati ottimali, migliorando precedenti teoremi di Kahane [9], Castro e Zuazua [3], Jaffard, Tucsnak e Zuazua [7] e di Ullrich [21]. Applichiamo poi questi risultati a problemi di osservabilità simultanea.
Integrability behaviour of the maximal partial sum of orthogonal series.