Newer applications of generalized monotone sequences.
Nombres de Pisot et fonctions moyenne-périodiques
Non-compact Littlewood-Paley theory for non-doubling measures
We prove weighted Littlewood-Paley inequalities for linear sums of functions satisfying mild decay, smoothness, and cancelation conditions. We prove these for general “regular” measure spaces, in which the underlying measure is not assumed to satisfy any doubling condition. Our result generalizes an earlier result of the author, proved on with Lebesgue measure. Our proof makes essential use of the technique of random dyadic grids, due to Nazarov, Treil, and Volberg.
Nonconvolution transforms with oscillating kernels that map into itself
We consider operators of the form with Ω(y,u) = K(y,u)h(y-u), where K is a Calderón-Zygmund kernel and (see (0.1) and (0.2)). We give necessary and sufficient conditions for such operators to map the Besov space (= B) into itself. In particular, all operators with , a > 0, a ≠ 1, map B into itself.
Nondoubling measure on Vilenkin group.
Nonfactorization in group algebras
Non-homogeneous strongly singular integrals
We study the mapping properties of a family of strongly singular oscillatory integral operators on ℝⁿ which are non-homogeneous in the sense that their kernels have isotropic oscillations but non-isotropic singularities.
Non-isotropic distance measures for lattice-generated sets.
We study distance measures for lattice-generated sets in Rd, d>=3, with respect to non-isotropic distances l-l.K, induced by smooth symmetric convex bodies K. An effective Fourier-analytic approach is developed to get sharp upper bounds for the second moment of the weighted distance measure.
Non-Lebesgue multiresolution analyses
Classical notions of wavelets and multiresolution analyses deal with the Hilbert space L²(ℝ) and the standard translation and dilation operators. Key in the study of these subjects is the low-pass filter, which is a periodic function h ∈ L²([0,1)) that satisfies the classical quadrature mirror filter equation |h(x)|²+|h(x+1/2)|² = 2. This equation is satisfied almost everywhere with respect to Lebesgue measure on the torus. Generalized multiresolution analyses and wavelets exist in abstract Hilbert...
Nonlinear Approximation by Trigonometric Sums.
Nonlinear Approximation Theory on Compact Groups.
Nonlinear Commutators and Jacobians.
Nonlocal Poincaré inequalities on Lie groups with polynomial volume growth and Riemannian manifolds
Let G be a real connected Lie group with polynomial volume growth endowed with its Haar measuredx. Given a C² positive bounded integrable function M on G, we give a sufficient condition for an L² Poincaré inequality with respect to the measure M(x)dx to hold on G. We then establish a nonlocal Poincaré inequality on G with respect to M(x)dx. We also give analogous Poincaré inequalities on Riemannian manifolds and deal with the case of Hardy inequalities.
Nonmonotone nonconvolution functions of positive type and applications
We present two sufficient conditions for nonconvolution kernels to be of positive type. We apply the results to obtain stability for one-dimensional models of chemically reacting viscoelastic materials.
Non-MSF Wavelets for the Hardy Space H²(ℝ)
All wavelets constructed so far for the Hardy space H²(ℝ) are MSF wavelets. We construct a family of H²-wavelets which are not MSF. An equivalence relation on H²-wavelets is introduced and it is shown that the corresponding equivalence classes are non-empty. Finally, we construct a family of H²-wavelets with Fourier transform not vanishing in any neighbourhood of the origin.
Nonnegative linearization for orthogonal polynomials with eventually constant Jacobi parameters
We study the nonnegative product linearization property for polynomials with eventually constant Jacobi parameters. For some special cases a necessary and sufficient condition for this property is provided.
Nonnegative linearization of orthogonal polynomials
Nonperiodic Sampling of Bandlimited Functions on Unions of Rectangular Lattices.
Non-separable bidimensional wavelet bases.
We build orthonormal and biorthogonal wavelet bases of L2(R2) with dilation matrices of determinant 2. As for the one dimensional case, our construction uses a scaling function which solves a two-scale difference equation associated to a FIR filter. Our wavelets are generated from a single compactly supported mother function. However, the regularity of these functions cannot be derived by the same approach as in the one dimensional case. We review existing techniques to evaluate the regularity of...
Non-similarity of Walsh and trigonometric systems
We show that in for p ≠ 2 the constants of equivalence between finite initial segments of the Walsh and trigonometric systems have power type growth. We also show that the Riemann ideal norms connected with those systems have power type growth.