Piecewise Linear Wavelets on Sierpinski Gasket Type Fractals.
Pointwise analysis of Riemann's "nondifferentiable" function.
Pointwise convergence for expansions in surface harmonics of arbitrary dimension.
Pointwise Fourier inversion of distributions on spheres
Given a distribution on the sphere we define, in analogy to the work of Łojasiewicz, the value of at a point of the sphere and we show that if has the value at , then the Fourier-Laplace series of at is Abel-summable to .
Pointwise smoothness, two-microlocalization and wavelet coefficients.
In this paper we shall compare three notions of pointwise smoothness: the usual definition, J.M. Bony's two-microlocal spaces Cx0s,s', and the corresponding definition on the wavelet coefficients. The purpose is mainly to show that these two-microlocal spaces provide "good substitutes" for the pointwise Hölder regularity condition; they can be very precisely compared with this condition, they have more functional properties, and can be characterized by conditions on the wavelet coefficients. We...
Poisson Summation, the Ambiguity Function, and the Theory of Weyl-Heisenberg Frames.
Polar wavelets and associated Littlewood-Paley theory [Book]
Polinomios ortogonales sobre la circunferencia unidad. Los casos C y D.
Polynomial approximation and twenty years later.
Polynomial approximation to integral transforms
Polynomial sequences generated by infinite Hessenberg matrices
We show that an infinite lower Hessenberg matrix generates polynomial sequences that correspond to the rows of infinite lower triangular invertible matrices. Orthogonal polynomial sequences are obtained when the Hessenberg matrix is tridiagonal. We study properties of the polynomial sequences and their corresponding matrices which are related to recurrence relations, companion matrices, matrix similarity, construction algorithms, and generating functions. When the Hessenberg matrix is also Toeplitz...
Positivity of Cotes Numbers at More Jacobi Abscissas.
Principe d'incertitude, bases hilbertiennes et algèbres d'opérateurs
Projecteurs invariants, matrices de dilatation, ondelettes et analyses multi-résolutions.
We show that (bi-orthogonal) wavelet bases associated to a dilation matrix which is compatible with integer shifts are generally provided by a multi-resolution analysis. The proof is done by studying the projectors which commute with integer shifts.
Properties of bounded orthonormal spline bases
Properties of refinable measures.
We give some new properties of refinable measures and survey results on their asymptotic normality. We also give a survey on the asymptotically optimal time-frequency localisation of refinable measures and associated wavelets.
Pseudo-orthogonal polynomials.
Quadrature formulas based on the scaling function
The scaling function corresponding to the Daubechies wavelet with two vanishing moments is used to derive new quadrature formulas. This scaling function has the smallest support among all orthonormal scaling functions with the properties and . So, in this sense, its choice is optimal. Numerical examples are given.
Quadrature formulas for rational functions.
Quantized orthonormal systems: A non-commutative Kwapień theorem
The concepts of Riesz type and cotype of a given Banach space are extended to a non-commutative setting. First, the Banach space is replaced by an operator space. The notion of quantized orthonormal system, which plays the role of an orthonormal system in the classical setting, is then defined. The Fourier type and cotype of an operator space with respect to a non-commutative compact group fit in this context. Also, the quantized analogs of Rademacher and Gaussian systems are treated. All this is...