Orthogonal Expansion of Vector-Valued Functions and Measures
Orthogonal Laurent polynomials and quadratures on the unit circle and the real half-line.
Orthogonal least squares solutions for linear operators.
Orthogonal polynomials.
Orthogonal polynomials and quadratic transformations.
Orthogonal Polynomials and Regularly Varying Sequences
Orthogonal polynomials and the Lanczos method
Lanczos method for solving a system of linear equations is well known. It is derived from a generalization of the method of moments and one of its main interests is that it provides the exact answer in at most n steps where n is the dimension of the system. Lanczos method can be implemented via several recursive algorithms known as Orthodir, Orthomin, Orthores, Biconjugate gradient,... In this paper, we show that all these procedures can be explained within the framework of formal orthogonal polynomials....
Orthogonal Polynomials, L2-Spaces and Entire Functions.
Orthogonal -polynomials related to perturbed linear form.
Orthogonal Trigonometric Schauder Bases of Optimal Degree for C(K).
Orthogonality Criteria for Compactly Supported Refinable Functions and Refinable Function Vectors.
Orthonormal polynomial vectors and least squares approximation for a discrete inner product.
Oscillating Multipliers for some Eigenfunction Expansions.
Oscillating multipliers on the Heisenberg group
Let ℒ be the sublaplacian on the Heisenberg group Hⁿ. A recent result of Müller and Stein shows that the operator is bounded on for all p satisfying |1/p - 1/2| < 1/(2n). In this paper we show that the same operator is bounded on in the bigger range |1/p - 1/2| < 1/(2n-1) if we consider only functions which are band limited in the central variable.
Osiris wavelets and set wavelets.
Padé and Hermite-Padé approximation and orthogonality.
Parabolic potentials and wavelet transforms with the generalized translation
Parabolic wavelet transforms associated with the singular heat operators and , where , are introduced. These transforms are defined in terms of the relevant generalized translation operator. An analogue of the Calderón reproducing formula is established. New inversion formulas are obtained for generalized parabolic potentials representing negative powers of the singular heat operators.
Partial sums of Fourier series
Partial Sums of Orthonormal Bases Preserving Positivity - and Martingales.
Permutations which avoid 1243 and 2143, continued fractions, and Chebyshev polynomials.