Exact solutions of the semi-infinite Toda lattice with applications to the inverse spectral problem.
Exceptional Sets and Wavelet Packets Orthonormal Bases.
Expansions for Gaussian processes and Parseval frames.
Explicit bounds of complex exponential frames.
Exponential Riordan arrays and permutation enumeration.
Exponentially decaying wavelets with uncertainty constants uniformly bounded with respect to the smoothness parameter.
Extensions of the Hardy-Littlewood inequalities for Schwarz symmetrization.
Factoring Wavelet Transforms into Lifting Steps.
Fast Fourier transform for rational systems.
Fejér–Riesz factorizations and the structure of bivariate polynomials orthogonal on the bi-circle
We give a complete characterization of the positive trigonometric polynomials on the bi-circle, which can be factored as where is a polynomial nonzero for and . The conditions are in terms of recurrence coefficients associated with the polynomials in lexicographical and reverse lexicographical ordering orthogonal with respect to the weight on the bi-circle. We use this result to describe how specific factorizations of weights on the bi-circle can be translated into identities relating...
Fine structure of the zeros of orthogonal polynomials. I: A tale of two pictures.
Finite Orthogonal Transforms and Multireolution Analyses on Intervals.
Finite-Dimensional Approximation of the Inverse Frame Operator.
FKN Theorem on the biased cube
We consider Boolean functions defined on the discrete cube equipped with a product probability measure , where and γ = √(α/β). This normalization ensures that the coordinate functions are orthonormal in . We prove that if the spectrum of a Boolean function is concentrated on the first two Fourier levels, then the function is close to a certain function of one variable. Our theorem strengthens the non-symmetric FKN Theorem due to Jendrej, Oleszkiewicz and Wojtaszczyk. Moreover, in the symmetric...
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.
Fonctions d'échelle interpolantes, polynômes de Bernstein et ondelettes non stationnaires.
The theory of convergence for (non-stationary) scaling functions and the approximation of interpolating scaling filters by means of Bernstein polynomials, allow us to construct a non-stationary interpolating scaling function with interesting approximation properties.
Fourier approach to homogenization problems
This article is divided into two chapters. The classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in the first chapter. Following a Fourier approach, we discuss some of the basic issues of the subject: main convergence theorem, Bloch approximation, estimates on second order derivatives, correctors for the medium, and so on. The second chapter is devoted to the discussion of some non-classical behaviour of vibration problems of periodic...
Fourier approach to homogenization problems
This article is divided into two chapters. The classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in the first chapter. Following a Fourier approach, we discuss some of the basic issues of the subject: main convergence theorem, Bloch approximation, estimates on second order derivatives, correctors for the medium, and so on. The second chapter is devoted to the discussion of some non-classical behaviour of vibration problems of periodic...
Fourier inversion of distributions on projective spaces
We show that the Fourier-Laplace series of a distribution on the real, complex or quarternionic projective space is uniformly Cesàro-summable to zero on a neighbourhood of a point if and only if this point does not belong to the support of the distribution.
Fourier transforms of Lipschitz functions on certain Lie groups.